Performance Analysis of Packet Schedulers Analysis of Packet Schedulers Layo Olumide Babagbemi ... (UMTS) network for ... call connection/burst level based on fluid flow …

Performance Analysis of Packet Schedulers Layo Olumide Babagbemi

Master Thesis

Computer

Engineering

2006 Reg. No: E3326D

DEGREE PROJECT

Computer Engineering

Programme Reg number Extent

International Master of Science in Computer Engineering E 3326D 30 ECTS Name of student Year-Month-Day

Layo Olumide Babagbemi 2006-06-07 Supervisor Examiner

Dr. Ernst Nordström

Prof. Mark Dougherty Company/Department Supervisor at the Company/Department

Department of Culture, Media & Computer Science,

Dalarna University

Gabor Fodor

Research and development,

Ericsson Kista Title

Performance Analysis of Packets Schedulers Keywords

Packets Schedulers, Overflow probability, Mean waiting

time.

Abstract:

The aim of this work is to model and investigate analytical techniques for studying

performance evaluation of packet schedulers in Universal Mobile Telecommunications

Systems (UMTS) network for enhanced uplink. A prototype system was developed for

call connection/burst level based on fluid flow ON/OFF Markov model and an

experiment was performed to evaluate packet scheduler performance. The simulation was

used to evaluate three types of schedulers namely; First-In First-Out (FIFO), Strict

Priority (SP) and Generalized processor sharing scheduler (GPS) in terms of mean

waiting time and overflow probability. Numerical result and theoretical consideration

([3] and [5]) reveals that the proposed analytical FIFO, SP and GPS model is accurate.

The overflow probability was low with all the schedulers, but lowest for GPS and PRIO

high priority class, meaning that FIFO, SP, and GPS all have potential for efficient

network utilization. Therefore, they can favorably support multi-services network. In

particular, the advantages of GPS makes it a preferable choice.

CONTENTS

Preface

1. Introduction

1.1 Background …………………………………………………………….. 1

1.2 Objectives …………………………………………………………….. 1

1.3 Limitations …………………………………………………………….. 1

1.4 Work method …………………………………………………………….. 2

1.5 Questions for investigation ………………………………………………. 2

1.6 Disposition …………………………………………………………….. 2

2. Problem formulation …………………………………………………….. 4

3. System overview …………………………………………………….. 6

3.1 Multi-service networks …………………………………………………….. 6

3.1.1 Circuit switching .………………………………………………… 6

3.1.2 Packet switching ……………………………………………. 8

3.1.3 Virtual circuit switching …………………………………………... 9

3.2 Packet schedulers …………..……………………………………………..11

3.2.1 Switch/Router ……………………………………………………..11

3.2.2 FIFO ...……………………………………………………………..11

3.2.3 Strict priority …………………………………………………….13

3.2.4 GPS ……………………………………………………………. 14

3.3 Resource allocation at call setup ………………………………........16

3.3.1 Call admission control……………………………………………..16

3.3.2 Routing …….…………………………………………………….18

4. Performance evaluation by analysis ………………………………….. 24

4.1 Evaluation of FIFO scheduler ………………………………………….. 24

4.2 Evaluation of strict priority scheduler ………………………………….. 26

4.3 Evaluation of GPS scheduler ………………………………………….. 28

5. Performance evaluation by simulation ………………………….. 30

5.1 Burst level simulation model …………………………………………... 30

6. Numerical results …………………………………………... 40

6.1 Considered packet schedulers ……………………………………………40

6.2 Examples and results …………………………………………………… 41

6.3 Result analysis …………………………………………………. …. 50

7. Conclusion …………………………………………………………… 51

References ………………………………………………………………. 53

Appendix ………………………………………………………………... 55

Preface

In recent years the mobile telecommunication system has experienced tremendous

growth. Improving on the existing method of transmission has been of great interest to

the industry. This was necessary in order to improve coverage, throughput and reduce

delay in transmission from the cell phone to base station in Universal Mobile

Telecommunications Systems (UMTS) network standard.

In a multi-service network [6, 7] the mobile users send and receive traffic that can be

classified into guaranteed and elastic traffic classes. The uplink connection to the base

station (Node B) is a process of receiving packets from the users and forwarding to the

Radio Network Controller (RNC). At the Node B, there is need for packet scheduler that

schedules the order of transmission of the user packets to the RNC.

We developed a model and analyzed the performance of the packet schedulers applicable

in the Node B. We designed a router/switch in an Internet Protocol (IP) or Asynchronous

Transfer Mode (ATM) network equipped with packet schedulers that determine the order

of packet transmission on the output communication links. Proper call admission control

(CAC) function relies on an accurate and efficient evaluation of queuing performance at

the output links.

A FIFO, SP and GPS scheduler type was simulated. FIFO validated against analytical

model, SP and GPS validation was done in [3], [5] literature respectively. Performance

metric was in terms of mean waiting time and overflow probability. We implemented

burst level traffic using the fluid flow Markov model. The queue size is assumed to be

infinite. Numerical results confirmed the accuracy of the proposed analytical FIFO, SP

and GPS models. FIFO has low overflow probability; efficient resource utilization. GPS

scheduling is flexibility in bandwidth allocation, priority by weight control, low inter-

arrival time variability. The SP high priority class receives excellent service with prio,

low overflow probability; high network utilization. The three schedulers are work

conserving and simple enough to implement efficiently.

Dedication

I dedicate this work first to God almighty for his love and support all through my study

period and, my parent Janet and Lawrence Babagbemi for their love assistance.

Acknowledgments

Special thanks to my supervisor Dr. Ernst Nordström for providing a great deal of effort,

time and patient through the work. Thanks also to Gabor Fodor at Ericsson Research in

Stockholm for his initiatives and brainstorm with my supervisor for the success of this

project.

I would also like to thank my HOD Prof. Mark Dougherty, my program coordinators Dr.

Pascal Reybrend and Hasan Fleyeh for their invaluable assistance in the course of this

work. Also, my appreciation goes to Siril Yella for his assistance.

Thanks to my brothers and sisters; Yomi, Tayo, Timi, Tosin and aunty Racheal.

Thanks to my pals Akin, Nosa, Appah, Kursad, Bola, Funsho, Emmanuel, Afeez, Segun,

Victor, David, Sam, Nadja, Maria, Hannah, and special regards to wonderful Colleen for

editing my work.

Sincere regards to Pastor Olaiya, Pastor Osarapo, Pastor Jegede, Pastor Camilla, Lief,

Pastor Strömberg for kind support in prayer. Finally, regards to all that might have been

omitted. You are all appreciated and not forgotten.

Layo Babagbemi

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Högskolan Dalarna Tel:+46(0)23 77 8000

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781 88 Borlänge url : www.du.se

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1. Introduction

1.1 Background

This master thesis is submitted in partial fulfillment of the requirement for the Degree of

International Master of Science in Computer Engineering, Högskolan Dalarna (Dalarna

University), Sweden. The research was carried out at the University provinces in the field of

mobile telecommunication network in support of improving cost effective services at the

Ericsson Mobile telecommunication industry.

1.2 Objectives

This work is to analyze the performance of packet schedulers as part of research on Enhanced

Uplink scheduling in a 3G base station at Ericsson Radio research, Kista. We model and evaluate

the performance of FIFO, SP and GPS packet schedulers. A system offered fluid flow traffic

from Markov on/off sources was developed for this purpose. The resource of the system is

bandwidth capacity. These studied schemes divide up bandwidth among flows that pass through

the router at each session arrival and departure.

1.3 Limitations

• We consider two traffic classes which could be more in reality.

• Three types of packet schedulers (FIFO, SP and GPS) scheme was considered for use at

the base station (Node B). In the future more or other schedulers can be introduced and

evaluated.

• The derivation and implementations of call admission control are for a single packet

multiplexing system.

• Per-Class GPS queuing.

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1.4 Work method

• This project and supervision was done in accordance to preset plans which includes:

• Literature review

• Problem definition

• Solution design

• Program development

• Simulation and testing

• Documentation

• Implementation was carried out in C programming language in a Network simulation

software package developed by Ernst Nordström®

. Weekly task reports and meetings

with my supervisor have proved to be an effective pattern for the success of this work.

1.5 Questions for investigation

We investigated two states space that gives acceptable Quality of Service (QoS) in terms of

mean waiting time or buffer overflow probability.

• The analytical model accuracy for FIFO, SP and GPS.

• Efficiency of each scheduler.

• Data lost rate probability in scheduled queue system.

• Improved model for uplink data rate without jeopardizing QoS and GoS.

1.6 Disposition

We embark on designing a decent scheduling model applicable in base station to effectively use

limited bandwidth capacity and maintain quality of service. This was achieved by developing

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and implementing different packets scheduler schemes. Performance evaluation was done in

three different scenarios specified in a network simulator.

The rest of this report is organized as follows. In Chapter 2, we define the problem and formulate

the solution. In Chapter 3, we describe multi-service networks and FIFO, SP and GPS scheduler

schemes, application of preventive call admission control for connection oriented ATM and

connectionless IP and routing per-connection for proper resource allocation at call setup. In

Chapter 4, we present performance evaluation by analysing FIFO, SP and GPS schedulers. In

Chapter 5, Simulation performance evaluation for burst level model is presented. In Chapter 6,

we compare numerical results for the considered packet schedulers. Finally, the report is

concluded in Chapter 7.

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2. Problem formulation

In order to achieved our goal of evaluating the performances of scheduler schemes. We study a

single packet multiplexing system consisting of total buffer space B [Mbit] and a packet

scheduler with service capacity C [Mbps]. The system is offered fluid flow traffic from Markov

ON/OFF sources from K classes. For simplicity, we assume K=2. Class j is described by:

• Number of sources: Nj

• Peak bit rate: pj [Mbps]

• ON to OFF transition rate: bj [s-1

]

• OFF to ON transition rate: aj [s-1

]

The performance of three types of packet schedulers (FIFO, strict priority and GPS) should be

evaluated by simulation and validated against an analytical model [2, 3, 4, 5]. The evaluation

should be done in terms of the mean waiting time and buffer overflow probability. The

admissible region is a region in the state space (N1, N2) that contains states that gives acceptable

Quality of Service (QoS) in terms of mean waiting time and/or buffer overflow probability. It is

important for clarity purpose to understand the expected Per-Class GPS system simulation and

the Per-Connection system in real life. In view of this, we show the illustration for GPS system

below in figure 1 and 2.

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c

1

2

Class 1

Class 2

Figure 1: Per–class GPS system (Simulation).

1,1

2 n2

1 n1

2,1

.

.

.

c

Class 1

Class 2

Figure 2: Per-connection GPS system (In real life).

.

.

.

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3. System overview

Our model is described to be applicable in a router/switch of an IP or ATM network. These two

networks are some example of multi-service networks that rely on reservation of resources for

real time traffic.

3.1 Multi-service networks

Multi-service network supports various types of services as it creates a unified network that

operates cohesively to promote efficiency, enhance service features, and save revenue. ATM/IP

designed as a multi-services network can accommodate various types of transport services.

Among other examples of services are circuit switching, Packet switching and virtual switching

which are related to this work. Traffic types on this network including data, voice, and video.

The matching of user services and traffic types within a single network and allowing service

providers to manage limited bandwidth resources is of great interest.

3.1.1 Circuit switching

Circuit switching (CS) network technology involves two end communication systems where a

channel is created and dedicated for the duration of a transmission. The connection is temporary

but dedicated in respective of how many switching devices the data are routed through. This

process involves 3 phases namely:

1. Circuit establishment

2. Data transfer

3. Circuit disconnect

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Circuit switching was originally developed for the analog-based telephone system in order to

guarantee steady, consistent service for two people engaged in a phone conversation. This type

of network is connection oriented with dedicated capacity and good for real time data

transmission. Each user has sole access to a circuit during network use. Take for instance

communication between two points A and E in a network. The connection between A and E is

provided using links that are shared between three other pieces of equipment, B, C and D as

illustrated in figure 3.

Network use is initiated by a connection phase, during which a circuit is set up between source

and destination, and terminated by a disconnect phase. After a user requests a circuit, the desired

destination address must be communicated to the local switching node B. In a telephone

network, this is achieved by dialing the number.

Node B receives the connection request and identifies a path to the destination E via an

intermediate node C. This is followed by a circuit connection phase handled by the switching

nodes and initiated by allocating a free circuit to C (link BC), followed by transmission of a call

request signal from node B to node C. In turn, node C allocates a link CD and the request is then

passed to node D after a similar delay. The same process takes place at node D which finally

allocates link DE and onward request passage to node E with associated delay. The circuit is then

established and may be used. In the duration of the use, resources in the intermediate equipment

at B, C and D and capacity on the links between the equipment are dedicated to the use of the

Node A Node B Node E Node C

AB CD BC DE

Node D

Figure 3: Connection by 4 links between two systems A and E

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circuit. After completion of the connection, a signal confirming circuit establishment is returned

directly back to node A with no search delays because the circuit is now in existence

(established). Transfer of the data in the message then begins. After data transfer, the circuit is

disconnected. The two notable shortcomings in the use of circuit switching for data connection

are:

• Delays for setting up a circuit connection can be high and much of the time the line is idle

making this approach inefficient.

• The connection provision is for transmission at a constant rate, which limits the utility of

the network.

3.1.2 Packet switching

Packet switching (PS) process in networks is the breaking of messages into small units of data

called packets and routed through the network based on the destination address contained within

each packet. Breaking communication down into packets allows the same data path to be shared

among many users in the network. Unlike circuit switching which requires the establishment of a

dedicated point-to-point connection, the packet-switched network contains in each packet a

destination address. Thus, all packets in a single message do not have to travel the same path. As

traffic conditions change, they can be dynamically routed through different paths in the network,

and they can even arrive out of order. This implies that, each packets flows in transmission

individually and can even follow different routes to a destination. When all the packets of a

message arrive at the destination, the packets are reassembled into the original message, which is

then passed onto the receiving terminal.

Packet switching is a good mode of data transmission because it permits some delay. Some

examples are TCP/IP and X.25. Today, using the IP protocol, packet networks are becoming the

norm for voice and video as it has always excelled at handling messages of different lengths, as

well as different priorities providing QoS. The use of packet switching for X.25 is significant as

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this also provide 'Virtual Circuits' to the user. This type of communication between sender and

receiver is known as connectionless oriented, no dedicated capacity but could be made

connection oriented by high level protocol TCP. Most traffic over the internet uses packet

switching and the internet is basically a connectionless network.

In fact, packet switching is now a dominating communication technique in computer networking

and telecommunications, where packets are individually routed between nodes over data links

which are available to be shared by many other nodes. Packet switching is useful for optimal

bandwidth management in a network, to minimize delay and to increase robustness of

communication. In circuit switching networks when traffic becomes heavy, some calls are

blocked until the load on the network decreases. But on a packet switching network, packets are

still accepted but delivery delay increases. In addition, priorities can be used on a packet

switching network. As such, if a number of packets are queued for transmission at a node, it can

transmit the higher-priority packets first while the lower-priority packets experience much more

delay, as employed in SP scheduling scheme of this work.

3.1.3 Virtual circuit switching

Virtual circuit is a logical circuit created within a shared network, in which data from a source

user is sent to a destination user over more than one real communication circuit during a single

period of communication. Virtual circuits can be classified into two types: Switched virtual

circuits (SVCs) and Permanent virtual circuits (PVCs). These are discussed in details later in

this section.

Further more, the virtual circuit is a connection oriented circuit suitable to hop-by-hop flow

control protocol in which QoS resources such as switch buffers and bandwidth are allocated at

each switch. A preplanned route is established before any packet is sent. Once the route is

established, all the packets between a pair of communicating parties follow this same route

through the network. It is somehow similar to circuit switching because the route is fixed for

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duration of the logical connection established, as such called virtual circuit. Each packet contains

a virtual circuit identifier as well as data [11]. No routing decisions are required as each node can

direct their packets on the pre-established route. VC-switching technique is applied in X.25,

ATM and Multiprotocol Label Switching (MPLS). The Internet computer network is entirely

built around the IP which is responsible for routing packets from one host to another.

The typical feature of a virtual circuit technique is that a route between stations is set up prior to

data transfer. This does not imply that the path is dedicated as in circuit switching as packet is

still buffered at each node and placed in a queue for output over a line. In the case of packet

switching routing is made only once for all packets using that virtual circuit. We hereby defined

the two types of virtual circuits in much detail:

• In Switched virtual circuits switching (SVCs) network, communication link is created on

demand and immediately terminated when transmission is completed. The process is in

the following phases: Circuit establishment, Data transfer, and Circuit termination. It is

used when data transmission between two devices is sporadic. This transmission

increases bandwidth use but is cost effective.

• Permanent virtual circuit (PVC) is a permanently created circuit available for data

transmission at all time. It is not terminated or re-established each time a data needs to be

sent as in the VCS. It has only one phase called data transfer. It is often used when data

transfer between two devices is constant and very efficient for connection between hosts.

This decreases bandwidth use but increases costs due to cost associated with constant

virtual circuit availability.

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3.2 Packet schedulers

Packet schedulers determine the order of packets transmission in a network and are located in the

Switch/Router.

3.2.1 Switch/Router

A device that forwards data packets along networks is called a router. It is connected to at least

two networks, commonly, Local Area Network (LAN) or Wide Area Network (WAN). Routers

are located at gateways, the place where two or more networks connect. It uses headers and

forwarding tables to determine the best path for forwarding the packets and use protocols to

communicate with each other configuring the best route between any two hosts. A Multiplexer in

the switch core of a router combines several packets for transmission over a single medium at the

output.

Packet schedulers in an ATM switch or an IP router with multiple input output link uses queue

management buffering strategies to perform its task effectively. Switching conflict would

definitely arise if there are no special mechanisms to control, the arriving packet at different

input port simultaneously attempting to gain access to the same output link. The buffer is a

suitable mechanism applicable to resolve switching conflicts. It can be places at three places in a

switch/router: at the inputs, at outputs or centrally. What does the buffer do? It simply stores the

arriving packets. However, we describe these following; FIFO, SP and GPS schedulers discipline

applied on the stored packets as presented in this work.

3.2.2 First-In, First-Out

First-In, First-Out (FIFO) queuing is the most basic queue scheduling discipline. In FIFO

queuing, all packets are treated equally by placing them into a single queue, and then servicing

them in the same order that they were placed into the queue. This Scheduling method processes

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packets according to their arrival order (to the ready queue). It does not emphases throughput

since long processes are allowed to monopolize CPU. FIFO queuing is also referred to as First-

Come, First-Served (FCFS) queuing. The packets are placed in queue order by the multiplexer

according to arrival time as shown below.

FIFO discipline is work conserving but there is no guarantee of services as this depends on the

timely behaviour of the other sources sharing the same multiplexer. In fact, if too many packets

arrives the buffer, there will be overflow and some packets will have to be dropped (losses). Also

as observed in fig.4a above, some packets may experience variable delay leading to change in

the time spacing between two successive packets. When that happens, packets may suffer

clumping or dispersion (see fig. 4b and 4c).

Figure 4a: FIFO

Flow 1

c

2 Flow 2

Flow 3

FIFO Queue

Multiplexer

1 1

3

2 3

Packet clumping

Server

Buffer

Figure 4b: First-In First-Out

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Reduction in the time distance between two successive packets is referred to as clumping and

increase in the time is called dispersion. These problems can be smooth by playout buffer

strategy at the receiver.

3.2.3 Strict priority

Strict priority queuing (SP) is the basis for a class of queue scheduling algorithms that are

designed to provide a relatively simple method of supporting differentiated service classes. SP

has separate FIFO queues used for each call class, which may contain one or more calls. The

queues have different priorities which control the order in which queues are served [8]. A low

priority queue is only served if there is no packet in the higher priority queues. In our system of

two buffers and classes, if necessary before onward transmission the higher priority class store

their data in Buffer 1. The low priority class store data in Buffer 2. The Buffer 1, has priority

access to the trunk and only the time-varying remains of bandwidth, if there is any, is available

for servicing Buffer 2 data [3].

Figure 4c: First-In First-Out

Packet dispersion

Server

Buffer

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The importance of this scheme in reality is when buffers of a FIFO queue begin to fill. The result

is large queue depths and the long queuing delays at the point of congestion. For example, if a

125 MB buffer on a 10 GbE WAN port fills to half capacity, that would introduce a 50 ms

queuing delay for any new incoming packet. Therefore, the switch can protect the critical delay-

sensitive packets by employing QoS-based buffering. The port buffer is divided into multiple

individual queues. Traffic sensitive to delay and delay variance, such as VoIP (Class 1) packets,

can be placed in a queue B1 that receives strict priority over the other queue B2 (Class 2) in this

model.

3.2.4 Generalized processor sharing

Generalized processor sharing (GPS) scheduling is the process of setting priority for packets

processing time, in a multiplexer by assigning different weight to determine the processing

Priority class 1

Server

Figure 5: Priority scheduling (PS)

Low priority queue

High priority queue

Priority class 2

B1

B2

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sequence of packets in queue. It is a work conserving scheduling discipline that can be regarded

as the limiting form of a weighted round robin policy [5] where traffic from session is treated as

an infinitely divisible fluid. It is widely considered to allocate bandwidth resources to

multiplexed traffic streams, effectively guaranteeing a certain level of QoS in a stochastic and

deterministic sense. In our analysis we focus on GPS scheduling with only two service classes

sources. The two-queue GPS system can be represented as shown in fig.6.

The sum of the buffer sizes for queue 1 and queue 2 is to equal the buffer of the FIFO scheduler

described earlier. (i.e. B=B1+B2). One of the important features of this ideal model is it ability to

provide isolation among different classes and at the same time allowing bandwidth sharing

among classes. Consider class K= (K1, K2) sources or sessions sharing a GPS server with rate c

and each session with its own queue. The question is how do we set the GPS weight (ø1, ø2)? We

determine the admissible set for fixed ø, which is the set of all (K1, K2) so as to satisfy the

statistical QoS of each connection/session. Each class is associated with sharing parameters

øi,1 ≤ i ≤ K (GPS weights) which determine the guaranteed service rate to the class:

cg n

j

i ∑=

=1 j

i

ø

ø (1)

c

1

2

Class 1

Class 2

B

B

Figure 6: GPS (B= B1+B2)

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Generally the received service by each class when K=2 is given by:

=

>−+=

=+

0)( ,

0)(,1))(( 0)(

tQc

tQtrccs

ji

jtQjji

i

j

φ

φφ (2)

where (x)+=maxx,0 and 1· is the indicator function, i ≠j are class indexes in the range 1 ≤ i,j ≤

2, rj(t) denotes the arrival rate of class j at time t, and Qj(t) denotes the queue length of class j at

time t.

This equation implies that the unused bandwidth by classes which are not backlogged will be

shared by all backlogged classes in proportion to their assigned weights. The size and shape of

the admissible region is very dependent on the weight, but it can be easily checked by the traffic

and QoS parameters of the classes.

3.3 Resource allocation at call setup

3.3.1 Call admission control

Call admission control (CAC) is classified as one of the three categories of preventive traffic

control. Traffic control is of great importance in multi-service networks. It is responsible for

maintaining the QoS and network availability while the network operators still achieves optimal

utilization of their network resources for maximum revenue in competitive environment. Call

admission control (CAC) is a preventive traffic control and enforcement scheme that decide for

each new call request, maybe to be accepted or if it must be rejected. It is used in circuit-

switched networks, ATM networks and QoS enhanced IP networks which provide QoS

guarantee. CAC decision making is based on three principles:

i. the QoS requirements for network calls.

ii. the GoS requirements for network call classes.

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iii. the call reward requirements.

Call admission control (CAC) plays a significant role in providing the desired quality of service

in wireless networks. Preventive call admission control (traffic and resource management) in this

work depends on the function of evaluated performance in terms of overflow probability and

waiting time. This helps to support a certain quality of services (QoS) requirements by

strategically limiting the number of call connections into the networks in order to reduce the

network congestion and call dropping. Good CAC schemes should balance the call blocking and

call dropping in order to provide the desired QoS requirements [9, 10].

Moreover, every network provider usually desires to make efficient use of their network. This

goal is aided by call admission control mechanisms, which performs its function by

understanding clearly exactly how much bandwidth is available. It checks the state of the buffer

for congestion or queue level and makes provisions for each call according to requirements

deciding acceptance or rejection of calls exceeding specification. This task is performed without

dissatisfying the two sub-functions which are Quality of Service (QoS) and Guarantee of service

(GoS).

• CACQoS decides at the time of call arrival, weather or not a new call should be admitted

in the network. A new call is admitted if and only if its QoS constraints can be satisfied

without affecting the QoS of the existing call in the network.

• CACGoS maintains guarantee of service and maximize the average rate. Charges are

different for different call types which mean different rewards for the network. GoS

decides which call is more economical to be carried on a path of the bandwidth.

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Finally, CAC uses traffic descriptors that specify traffic characteristic and QoS requirements to

aid its decision making. Traffic characteristics are peak cell rate, Sustained cell rate, maximum

burst size and so on. QoS requirements are tolerable cell loss, cell delay and delay variation.

3.3.2 Routing

Routing is a packet-forwarding process from a source to a destination among subnetworks. A

router is a device connected to at least two networks that forwards data packet along LAN or

WAN. Circuit-switched networks routing algorithms are also used for packet-switched networks

with virtual circuits, such as ATM networks and QoS enhanced IP networks. In circuit switched

networks, the network reserves resources before call setup and the usage of resources is enforced

through out the lifetime of calls.

Assume the network traffic is comprised of K call classes. Call class j is described by

• Origin destination pair

• Call arrival process parameters

• Call holding time distribution parameters

• Link bandwidth requirement [ ]Mbpsbs

j

• Reward parameter ( )∞∈ ,0jr

• Set of alternative routes jW

If the call arrival process is Poisson with rate jλ and the call holding times are exponentially

distributed with mean jµ/1 for the class-j.

The following are the different types of routing algorithms proposed for circuit switched

networks:

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• Fixed non-alternative routing.

• Fixed load sharing routing

• Sticky random routing

• Fixed alternative routing

• Least Loaded routing

• Markov decision process routing.

Fixed non- alternative routing: Call is routed only on one path between source and destination. If

the path is found busy then the call is rejected. Trunk reservation may be used to protect the wide

band calls from overload of narrow band calls.

Fixed load sharing routing: Call is routed according to a set of fixed load sharing probabilities

which assigns probabilities for selecting different routes for a call from each class. Calls are

offered to one path, and if the path is busy, the call is blocked. Trunk reservation may be used to

protect the wide band calls from overload of narrow band calls.

Sticky random routing: Call is offered to the direct path at first. The call is established if the path

is available. Otherwise, the previous chosen alternative path is offered the call and the call is

established if the path is available. If it is not, the call is blocked and the alternative path is

reselected. The new alternative route is used by the next call that finds the direct path busy.

Trunk reservation and external blocking (external blocking is a procedure where only a fraction

of the calls rejected on the direct path are allowed to request an alternative path) can be used to

obtain fairness between the call classes.

Fixed alternate routing: Algorithm chooses paths for new calls according to fixed alternative

sequences. Trunk reservation and external blocking can be used. The first path in the sequence to

be tried is the direct path. If it is busy, the remaining paths are tried, in order, until a path that is

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able to accept the call is found, or there is not more paths in the sequence in which case the call

is rejected [8].

Least loaded routing: The call is first offered to the direct path. If it is busy, an alternative path is

searched for according to a state-dependent rule. If no such path is found the call is rejected. The

state-dependent routing rule selects a path with sufficient capacity that also has the largest free

capacity of its bottle neck link. The bottle neck link is the link with least free capacity along the

path [8]. Trunk reservation and external blocking may be used to protect direct routed calls and

wide band calls.

Markov decision process routing: This is also a state-dependent alternative routing. It is a set of

gain functions which control the selection of routes for new calls. The gain ( )π,ygk

j measures,

for a given call class j, the increase in long term rewards when choosing particular path k in

network state y under routing ruleπ . The routing rule selects the path which has the largest

positive gain for the new call. If no path has the positive gain, the call is rejected. Markov

decision process does not use trunk reservation or external blocking. In order to reduce

complexity, the network is decomposed into a set of links which changes state independently.

Routing in ATM networks

PNNI is a dynamic routing protocol for ATM. PNNI is dynamic because it learns the network

topology and accessibility information and automatically adapts to network changes by

advertising topology state information using metrics and attributes. For large-scale or growing

ATM-based networks, hierarchical PNNI uses a number of mechanisms that enable multilevel,

flexible routing hierarchies. The ability to treat a group of switches as a single logical group node

(LGN) significantly improves scalability which is one of its main goals. Scalability is achieved

in PNNI by creating a hierarchical organization of the network, which reduces the amount of

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topological information PNNI has to store. It also reduces the amount of PNNI traffic and

processing. The routing component of the PNNI protocol specifies how the signalling request

and subsequent data connection are routed through the ATM network to establish point-to-point

or point-multipoint connections.

The two interpretations of the PNNI acronym suggest different applications: Private Network

Node Interface refers to routing between ATM switches in a private network. Private Network-

Network Interface refers to routing between private ATM networks. PNNI organizes

neighbouring nodes to form peer groups by exchanging their peer groups identifier (PGIDs)

through Hello packets using a protocol that enable nodes to know each other. Hello protocol

exchange occurs over logical links between one or more border nodes across the peer group

boundary. PNNI create and distribute topology database that enable nodes to exchange

information using PTSEs (PNNI Topology State Elements).

Each peer group has a node called the peer group leader (PGL). PGL per peer group represent its

group as a single node in the parent peer group. Call establishment by PNNI consist of two

operations. That is, path selection and the setup of the connection state at each point along the

path and encoded as Designated Transit List (DTL). Path routing obeys source routing

instruction and computation is on an on-demand basis but no standardized algorithm is specified.

We assume PNNI employs state-dependent dynamic routing strategy.

Routing in IP network

IP flow is a connectionless network transmission between IP subnetworks. Its unique network

addresses enhanced their link up for Internet service purpose. The best-effort service routing in

Internet is managed by dividing the IP subnetworks into Autonomous Systems (ASs). An

example of AS is a Campus network. Special routing protocols are used within the AS’s and

between AS’s called intra-domain routing and inter domain routing protocols respectively.

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o The Intra-domain routing protocols are either based on distance vector routing or on link

state routing. The protocols use some algorithm to compute the shortest path routes

between the source and the destination.

o In Inter-domain routing the objective is to find loop-free paths which can reach the

destinations. It does not bother finding optimal paths.

The two basic activities in routing are:

• Determining optimal routing paths (determining optimal routing path can be very

complex).

• Transporting packets through an inter-network (Packet switching is straightforward).

These are the main processes used by Internet hosts to deliver packets. Internet uses a hop-by-

hop routing model, which means that each host or router that handles a packet examines the

Destination Address in the IP header, computes the next hop that will bring the packet one step

closer to its destination, and delivers the packet to the next hop, where the process is repeated. To

make this work, two things are required. First, routing tables match destination addresses with

next hops. Second, routing protocols determine the contents of these tables.

Distance vector routing: Distance vector routing decision is computed by considering distance in

terms of hops and a vector (direction). Routing algorithms generate routing tables that contain

route information to make the process easy. Destination/next hop in the network tell a router that

a particular destination can be reached optimally by sending the packet to a particular router

representing the next hop on the way to the final destination. When a router receives an incoming

packet, it updates by checking the destination address and then attempts to associate this address

with a next hop.

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Link state routing: A link-state advertisement is another example of a message sent between

routers. It informs other routers of the state of the sender's links. Link information also can be

used to build a complete picture of network topology to enable routers to determine optimal

routes to network destinations. Link-state protocols rely on two mechanisms: reliable

dissemination of link-state information [8], and the calculation of routes from the sum of all

accumulated link-state knowledge.

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4. Performance evaluation by analysis

4.1 Evaluation of FIFO scheduler

In this section we evaluate the performance of a single multiplexer system of FIFO queue offered

fluid flow traffic from k classes of on/off sources. An exact evaluation of the fluid is possible

when the class of arrival processes is restricted to the case where the arrival rate can be modelled

as Markov process. The traffic class is described by:




]


]

We consider an irreducible persistent continuous-time Markov process, with infinitesimal

generator M, and countable state-space S. Let sii ∈

→

= ππ denote the corresponding equilibrium

probabilities, i.e., →

π satisfies →

π M = 0 and ∑ iπ = 1.

Assume the buffer of size B Mbits rate of receiving information is at di whenever the process is

in the state i and that it empties at a rate of C.

dx/dt = fin - C when

0 when x = B and fin > C

0 when x = 0 and fin < C

0 < x > B

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Let D denote the diagonal matrix with entry (i, i) equal to di - C, and define

∞→=

ti xF lim)( Prrate process in state i and buffer contents not exceeding x. (3)

From [2]-[12], it is known that Fi(x) S ∈i satisfies the following equation

( ) ( ) .MxFDxFdx

d= (4)

For this purpose, we assume an infinite buffer and estimate the cell-loss probability for a buffer

of size B by the probability of the queue length exceeding B. If we add the extra condition that

the arrival rate process is finite-dimensional and time-reversible, then MD-1

is known [12], to

have a basis of eigenvectors and the solution to equation above can be written as

( ) i

x

i

N

i

veaxF iλ

1=∑= (5)

where λi are the eigenvalues of MD-1

, νi are the corresponding left eigenvectors, and N is the

number of states in S. Moreover, for a stable infinite buffer system, we must have ai = 0 for λi > 0,

and the boundary conditions are expressed as

Fi (0) = 0 for di > C,

ai = 0 for i fulfilling λi > 0. (5b)

when F(x) is found, the queue length distribution is easily derived.

The exact analytical model are computation demanding when the number of classes k is high

(K>2). The size of the state space is )1(1

+= ∏ =

c

i is NN . The computational complexity relies

more on the calculation of the coefficients ai from the boundary conditions. The coefficient is

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deduced by solving a set of Ns linear equations. Gauss elimination can be applied to solve this

system of equation. The complexity is in the order of ).( 3

sNO Therefore the complexity of the

fluid flow model increases very fast with increasing number of classes C and the class sizes Ni.

4.2 Evaluation of strict priority scheduler

In this sub-section we evaluate the performance of strict priority offered Markov fluid flow

traffic source from two classes. The presentation is based on Elwalid and Mitra [3] propose

approximation formulae for the buffer occupancy distribution. The sources which belong to a

high priority class share a FIFO buffer which has priority access to the trunk. A low priority class

of sources has a separate FIFO buffer, which receives the residual bandwidth, if any. The service

guarantees for both classes may be regulated by administering admission control. The key

element of this analysis is a characterization of the outflow of the high priority buffer as another

Markov-modulated fluid source.

Let Ωt denote the output process of B1 and RΩ (t) the rate of the process at time t, Also the sum

of the rates of the fluid generation at time t by the sources of class 1 and 2 is R∑1(t) and R∑2(t)

respectively. Let the trunk capacity be at constant rate c. The content of the two buffers are given

by B1(t) and B2(t) as indicated in the figure below. Therefore this sample path equation describes

the system:

.(6)...................................................................... 0)( if c- (t)R)( 111 >= ∑ tBtBdt

d

= [ ]+

∑ c- (t)R 1 if B1(t) = 0

Let [x]+

denote the positive part of x. Also,

RΩ (t) = c if B1(t) >0 …………………………………………......(7)

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= R∑1(t) if B1(t) = 0.

Now c - RΩ (t), a nonnegative quantity, is the channel bandwidth available for servicing Buffer

2. Hence,

)........(8........................................ 0)( if (t)R - c- (t)R)( 122 >= Ω∑ tBtBdt

d

= [ ]+

Ω∑ (t)R - c- (t)R 2 if B2(t) = 0 ……………………………... (9)

Let each class to be from independent sources. Each source is a Markov modulated fluid

characterized by (M(j),

)( jλ ) where M(j),

is the generator of the Markov chain and )( jλ is the

vector state dependent rate of fluid generation by the source. The homogeneity reduces

computational complexity and makes the description of the technique simpler.

B1(tB2(t

1

K1

2 . . .

.

.

.

1

2

K2

Trunk

Buffer Buffer

RΩ(tHigh Priority, Class 1, sources

Low Priority, Class 2, sources

Figure 7: Strict priority system.

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The output process is model as another Markov modulated fluid source (M(Ω),

)(Ωλ ). The number

of states of this source is typically high. The idea in the construction is that at equilibrium

Buffer-1 is typically empty for high fraction of time. For instance, if the cell loss probability for

the higher priority services is bounded by 10-9

, the probability that the buffer is not empty can be

as small as 10-3

– 10-5

. This is not to say that the throughput is necessarily small while the buffer

is empty. On the contrary, in a fluid model if the buffer is empty then it remains so as long as the

aggregate source rate is not more than the outgoing channel rate.

4.3 Evaluation of GPS scheduler

In this sub-section we evaluate the performance of fluid flow in two-queue GPS system. For i =

1,2, the session i source, is a Markov modulated fluid process with irreducible generator M(i)

on

state space S(i)

= 1,…,N(i)

, and rate vector λ(i)

= )(

1

iλ ,…, )(

)(

i

iNλ .

If we consider øi, taking i =1, 2 as the GPS assignment for the two sessions (see illustration fig.8

below). We assume that ø1 + ø2 = 1, that means each session is guaranteed a minimum service rate

Figure 8: A two-queue GPS system

c

1

2

Class 1

Class 2

B1

B2

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gi = øic. For i =1,2, let λ i denote the average input rate of session i source. The condition for

stability in the system is that we have 1λ + λ 2 < c. For i =1,2, let ri (t) ∈ )(

1

iλ ,…, )(

)(

i

iNλ denote

the rate of session i arrival at time t, and for any τ < t, define Ai (τ ,t) = ,)( duurt

i∫τ the

(cumulative) arrival process for session i. Similarly, let si(t) denote the service/departure rate of

session i at time t, and define Si(τ ,t) = ,)( duust

i∫τ the session i departure process. In addition, let

Qi(t) denote the session i backlog at time t. Then, we have Qi(t) = supr t≤ Ai (τ ,t) - Si(τ ,t).

The following equation path describes the dynamics of the GPS system:

[ ] )10...(..................................................1)(()()( 0)(22111 2 =+−+−= tQtrcctrtQ

dt

dφφ

[ ] )11(..................................................1)(()()( 0)(11222 1 =+−+−= tQtrcctrtQ

dt

dφφ

Where (x)+

= maxx, 0 and 1 • is the indicator function. It can be deduced from the GPS

definition that, if both queues are not empty at time t, then s1(t) = g1 = ø1c, s2(t) = g2 = ø2c. If one

of the sessions has an empty queue at time t, then the other session in addition to its guaranteed

service rate will receive the residual service from that session. An upper and lower bound for the

overflow probability is proposed by [5] Presti and Towsley.

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5. Performance evaluation by simulation

5.1 Burst level simulation model

In the hierarchical model of traffic in network, burst layer is used to model the burst arrival

process. The burst layer is an intermediate traffic layer between the call layer and packet layer. It

operates in the time scale of milliseconds.

Performance of network evaluation based on burst layer is determined by the QoS and consist of

end-to-end packet loss probability, delay and delay variability (jitter). We simulate and evaluate

performance by burst level model for this three following packet schedulers; FIFO, Strict priority

and GPS.

Call level

Burst level

Packet level

ms

s

Traffic levels

µs

Figure 9: Traffic level

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Simulation method

We considered a system offered fluid flow traffic from Markov ON/OFF sources from K

classes. We assume K = 2 class j is described by:




]


]

Figure10: State transition diagrams for infinite call queuing system

ON OFF

a

b

ON OFF

(BA) (BD)

Figure10b:

Figure: 10a

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The figure 10a above represents the burst arrival and departure process. The BA and BD are the

burst arrival and departure time respectively. Interval between BA and BD is the active ON state,

when it transmits information at a peak rate and the interval between BD and the next BA is a

silent OFF state. The duration of the ON and OFF periods are assumed to be exponentially

distributed. The burst arrival process involves the time the burst arrives and the expected time of

departure depending on the service type. The process all together can be called an event.

Let the arrival of burst be viewed as a stream of fluid traffic, characterized by a flow rate (bit per

second), so that a traffic count is replaced by a traffic volume [8] . Inflow of traffic into the

buffer can be represented as shown in fig. 11. The traffic descriptor (peak rate, mean rate,

maximum burst size) can be enforced by two token buckets, one supervising the mean rate and

the maximum burst size. The content of the buffer depends on the inflow and outflow of fluid. If

the inflow is greater than outflow, congestion and overflow might occur. The data transmission

by the ∑ Ni sources is received by a finite buffer of size B Mbits with a maximum output rate of

C Mbps. The buffer is modelled as fluid reservoir with a hole in the bottom and arriving

information is modelled as a fluid running into the reservoir. If fin is the inflow rate, and x is the

buffer content, then the change in buffer content is given by

dx/dt = fin - C when

0 when x = B and fin > C

0 when x = 0 and fin < C

0 < x > B

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In general, a fluid simulation assumes that the inflow fluid remains (roughly) constant over long

time periods. Traffic fluctuations are modelled by events signalling change of flow rate.

Computing is made much easier as these changes can be assumed to happen far less frequent

than cell arrival process. In context of queuing, it is easy to manipulate fluid buffers. Thus,

deterministic services rate statistics can be readily computed. The time it takes to clear the buffer

content is the waiting time.

FIFO simulation

The central idea is to simulate different network scenarios for packet transmission. We compute

FIFO burst event analysis function in a network simulator and modify the network scenario

according to standard specifications for limited call classes (2-class traffic) for simplicity.

outflow

Buffer

inflow

c Buffer level

Figure 11

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o Current buffer size (x) – the buffer state at a point in time.

o Change in buffer size (∆x) – Increment of the inflow might cause the buffer content to

increase if the outflow rate is lesser than the inflow rate at a point in time. This

automatically results in change in the buffer size (Buffer state).

o Buffer size – Is the total buffer capacity in mega bytes.

o Free buffer – This is the estimated free space in the buffer as of the time under

consideration.

The buffer system is said to be busy when it is at its full state. At this point, inflow can only be

admitted depending on the current rate of outflow. Beyond this state the buffer is considered

saturated. If the packets stay in longer and saturation persists then overflow of the buffer will be

experienced. This can be referred to as packet loss. The time taken to serve (clear) the current

buffer is called the waiting time. These occurrences are of great importance (in this work) for

performance analysis. The described process can be represented graphically as shown in fig. 13:

Free buffer

Inflo

X_Buffer Size

y_Buffer Size

∆x

Buffer size

Figure 12: A typical Buffer

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In the FIFO buffer of size B and link with capacity C system, inflow is admitted by a preventive

CAC. The FIFO burst event analysis function updates the state of the buffer and to accumulates

the period τk, k=1,2,3..., when the buffer is saturated (i.e at its maximum level). The new burst

event is assumed to occur at ty and the previous burst event is assumed to occur at tx. The

function determines the buffer state at ty. This is done by first determining if the sum fin of all

fluid flows from the active sources (i.e. that are in their ON states) is smaller or larger than the

link capacity C:

B

t x

Buffer content

time

c

time

No free buffer

Saturation time

I

II

t x

I

II

ON OFF

Saturation Increasing inflow

t y

t y

Inflow

Figure 13: Graphical representation of a Buffer

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• Case I: fin ≤ C

• Case II: fin > C

where

∑=

=K

i

iiin pnf1

where ni denotes the number of active class i sources at time tx.. In case I only the buffer state

was updated. In case II the buffer state is updated, and in addition, the buffer saturation time is

added to a summation variable. Note that, depending on the level of the buffer at time at tx, the

total inflow may be too small for the buffer to saturate before time ty. Only when the buffer

saturates before at ty, the buffer saturation time will be larger than zero.

The buffer overflow probability is estimated from the measured buffer saturation time τk and the

time T of the total measurement period:

∑=>k

kT

BQP τ1

)(

This is the probability that, if the buffer is inspected at an arbitrary point in time, the buffer is

found to be held at its maximum.

The mean waiting time is estimated by Little’s law:

m

NW

q=

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where Nq denotes the average queue size and m denotes the mean offered bit rate. The average

queue size Nq is measured in function burst event analysis function. The mean offered bit rate m

is determined in the simulation process.

GPS simulation

We considered decomposition of a basic FIFO buffer as two queuing buffer system. The sum of

the buffer sizes for queue 1 and queue 2 should equal the buffer of the FIFO scheduler (i.e.

B=B1+B2). We have two regions in GPS scheduling, depending on if the total inflow fin,i of class

i is smaller or larger than the total outflow fout,i of class i:

• Case I: fin,i ≤ fout,i

• Case II: fin,i> fout,i

The principles for FIFO also apply to every GPS sub-queue. That is, when in region I only the

buffer level of queue i is updated. When in region II, we update the buffer level but also count

the time period τi,k when the buffer is saturated. The total outflow of class i for K=2 is

determined from the GPS weights of the active classes at time tx:

=

>−+=

=+

0)( ,

0)(,1))(( 0)(,

,tQc

tQtfccf

ji

jtQjinji

iout

j

φ

φφ

where (x)+=maxx,0 and 1· is the indicator function, i ≠j are class indexes in the range 1 ≤ i,j ≤

2, and Qj(t) denotes the queue length of class j at time t.

The buffer overflow probability is estimated from the measure of the buffer saturation time τk

and the time T of the total measurement period:

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∑=>k

kiiiT

BQP ,

1)( τ

This is the probability that if the buffer is inspected at an arbitrary point in time, the buffer is


The mean waiting time for class i is estimated by Little’s law:

i

iq

im

NW

,=

Where, Nq,i denotes the average queue size and mi denotes the mean offered bit rate of class i.

The average queue size Nq,i is measured in function GPS burst event analysis function. The mean

offered bit rate mi is also determined and used in the simulation.

Strict priority simulation

The strict priority scheduler is offered traffic from two classes. Class 1 is given strict priority

over the class 2 meaning that the class 2 receives any left over service capacity not used by class-

1. Each class has their own buffer. The sum of the buffer sizes for the queues is equal the buffer

of the FIFO scheduler (i.e. B=B1+B2).

The principles for FIFO also apply here to every priority sub-queue. That is, when in region I

only the buffer level of queue i should be updated. When in region II, we should update buffer

level but also count the time period τi,k, the buffer is saturated.

We have the following maximum outflows for each class [2]:

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>

≤=

−=

=

CC

Cff

fCf

Cf

in

out

outout

out

in,1

in,11,

1,

1,2,

1,

f if

f if ~

where

~

denotes the actual out flow from the buffer of class 1 and iiiin pnf =, is the inflow of class i at

time at time tx.

The buffer overflow probability is estimated from the measure of the buffer saturation time τi,k

and the time T of the total measurement period:

∑=>k

kiiiT

BQP ,

1)( τ

This is the probability that if the buffer is inspected at an arbitrary point in time, the buffer is


The mean waiting time for class i is estimated by Little’s law:

i

iq

im

NW

,=

where Nq,i denotes the average queue size and mi denotes the mean offered bit rate of class i. The

average queue size Nq,i is measured in function prio burst event analysis function. The mean

offered bit rate mi is determined and applied in simulation as in the equation above.

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6. Numerical results

6.1 Considered packet schedulers

The considered packet schedulers in the numerical experiments are FIFO, Strict priority (SP) and

GPS scheduler. Simulation results accuracy was confirmed by comparison with either analytical

model or literature.

The two performance evaluation parameters are mean waiting time and buffer overflow

probability.

• FIFO – Packet scheduler based on Markov ON/OFF fluid flow traffic proposed in

subsection 3.2.1.

• SP – Packet scheduler based on Markov ON/OFF fluid flow traffic with strict priority

assignment to one of the class over the other. See subsection 3.2.2

• GPS - Packet scheduler based on Markov ON/OFF fluid flow traffic by GPS weight

assignment for sever sharing among classes (3.2.3).

• We carried out investigation in different network scenario to compare the proposed

analytical model with simulations results. Also, to compare the three packet schedulers in

terms of mean waiting time and buffer overflow probability.

The FIFO algorithm forms the basis queue model. It performs no shaping or rearranging of

packets. It simply links packets onward with the capacity in the order of their arrival. However, it

does not satisfy the sharing of bandwidth capacity according to desired interest. GPS and SP

compensate for the function of placing and serving the packet by arrival time discipline.

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FIFO packet scheduler works like this, when the traffic of fluid flow of class j arrives at the

buffer of a size limit (buffer size). The buffer updates it content by inflow packets and outflow a

link queue by placing the first arriving packet at the head of the queue, followed by the next. The

process is ruled by this condition: if inflow is smaller or equal to the link capacity C, the packet

is received at the buffer and placed on queue according to it arrival time. Otherwise, if the inflow

is greater than the link capacity C, congestion is likely to happen and persistent saturation (full

buffer) will result to buffer overflow. The procedure ends when the buffer overflow probability

is estimated from the measured buffer saturation (packet count) time and the time of the total

measurement period. Also, the mean waiting time for each class j is estimated.

The strict priority works as follows, when the call-class j request is received. The call-class j with

priority is queue in one buffer and the low priority is queue in the second. The high priority

packet gets the complete allocation of the capacity and the low priority buffer only outflow

packets if and only if the outflow from the SP is not great or equal to the capacity. This model is

split into two queues, numbered 1 and 2 (B1+ B2 = B) starting from the most prioritized band (0)

and finishes at the least (1). The mechanism of the FIFO applies here as well, with the procedure

stopping by estimating overflow probability and the mean waiting time for each class- j.

The GPS is a decomposed FIFO queue with similar traffic inflow but the packet scheduling

principle makes the difference. GPS assign weight to the active call-class j and outflow packets

according to the allocated ratio for each active call-class j. The process round up by overflow

probability and mean waiting time estimation.

6.2 Examples and results

The performance analysis for the packet scheduler when the total offered traffic is measured

by ∑=

=K

j

jjin pnf1

. The packet multiplexing system consisting of total buffer space B [Mbit] and

a packet scheduler with service capacity C [Mbps], offered fluid flow traffic from Markov

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ON/OFF sources from K classes. For simplicity, we assume K=2. The algorithm-specific

parameter settings were determined heuristically based on simulation and experiment plan

scenario. One simulation run consists of an initial ‘warm up’ period, followed by a number of

adaptation period of an event type at a measurement period. We simulate three different traffic

scenarios for analysis. Table-1 shows the specification of the each simulation. The traffic class j

is described by the following parameters:




]


]

• GPS weight φ

Table 1. Three different network scenarios simulation specifications.

i Ni pi ai bi φ

1

16

8

0.5

0.5

0.5161

Balanced load

Sim-1

2

20

6

0.5

0.5

0.4839

1

28

8

0.5

0.5

0.9032

Class-1 Overload

Sim-2

2

4

6

0.5

0.5

0.0968

1

3

8

0.5

0.5

0.0976

Class-2 Overload

Sim-3

2

37

6

0.5

0.5

0.9024

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The performances metric is in terms of mean waiting time and overflow probability. FIFO

simulation results were validated against analytical model FIFO. GPS simulation results where

validated against FIFO for one class (K=1). We also validated the GPS implementation against

the simulation results by Presti and Towsley [5]. SP simulation validation was done against the

simulation results by Elwalid and Mitra [3].

Graphs:

The three simulation plots for overflow probability and mean waiting time are presented in the

next page. Each page contains the overflow probability and mean waiting time per class for GPS,

SP and FIFO for each simulation respectively.

o Page 44 present overflow probability per class for simulation -1

o Page 45 present mean waiting time per class for simulation -1





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Simulation-1 (Fig.14-17) Note: In all simulation the GPS coefficient for each class is set to the

per-class fraction of the mean load.

Class 1 overflow probability (sim_1)

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

P(Q

>B

)

Analytical_fifo

FIFO

Prio

GPS

Figure 14: Class-1 overflow SP, GPS, FIFO simulation and analytical FIFO.

Class_2 overflow probability (Sim_1)

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

P(Q

>B

) Analytical

FIFO

Prio (SP)

GPS


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Class_1 mean waiting time (sim_1)

0

0,001

0,002

0,003

0,004

0,005

0,006

0,007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

Wa

itin

g t

ime

FIFO

Prio (SP)

GPS

Figure16: Plot of FIFO and Class-1 SP, GPS mean waiting time vs the buffer size.

Class_2 mean waiting time (Sim_1)

0

0,002

0,004

0,006

0,008

0,01

0,012

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

Wa

itin

g t

ime

FIFO

Prio (SP)

GPS

Figure17: Plot of FIFO and Class-2 SP, GPS mean waiting time vs the buffer size.

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Simulation-2 (Figure 18-21) Note: In all simulation the GPS coefficient for each class is set to

the per-class fraction of the mean load.


0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

P(Q

>B

) Analytical

FIFO

Prio (SP)

GPS


Class_2 overflow Probability (Sim_2)

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

P(Q

>B

) Analytical

FIFO

Prio (SP)

GPS

Figure19: Class-2 overflow SP, GPS, FIFO simulation and analytical FIFO.

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Class_1 mean waiting time (Sim_2)

0

0,001

0,002

0,003

0,004

0,005

0,006

0,007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

Wa

itin

g t

ime

FIFO

Prio (SP)

GPS

Figure 20: Plot of FIFO and Class-1 SP, GPS mean waiting time vs the buffer size.

Class_2 Mean waiting time (Sim_2)

0

0,01

0,02

0,03

0,04

0,05

0,06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

Wa

itin

g t

ime

FIFO

Prio (SP)

GPS


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Simulation-3 (Fig. 22-25) Note: In all simulation the GPS coefficient for each class is set to the

per-class fraction of the mean load.


0

0,5

1

1,5

2

2,5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

P(Q

>B

) Analytical

FIFO

Prio (SP)

GPS



0

0,5

1

1,5

2

2,5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

P(Q

>B

) Analytical

FIFO

Prio (SP)

GPS


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0

0,002

0,004

0,006

0,008

0,01

0,012

0,014

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

Wa

itin

g t

ime

FIFO

Prio (SP)

GPS



0

0,0005

0,001

0,0015

0,002

0,0025

0,003

0,0035

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Buffer size

Wait

ing

tim

e

FIFO

Prio (SP)

GPS


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6.3 Result analysis

In order to check the accuracy of the analysis, twenty iterate independent simulations were run

for specified parameters. We have compared the accuracy of the FIFO simulation with the

analytical FIFO model. The results shown from the graphs produce the same rate of change of

overflow probability with buffer size. We validated the GPS and SP against the simulation

results in [5] and [3], respectively. The results were similar but more interesting as we deduced

the following facts:

• The FIFO simulation result proves the accuracy of the analytical model.

• The high priority class receives excellent service with PRIO.

• For balanced load case the PRIO class 1 overflow probability is zero, and the PRIO class

2 overflow probability is the same for FIFO

• GPS has lower overflow probability than FIFO for all load cases.

• GPS has higher waiting time for the low load class in the unbalanced load cases.

• GPS has lower waiting time for the high load class in the unbalanced load cases.

• There is a reciprocal dependence between overflow probability and waiting time.

7. Conclusion

In this paper, we studied packet schedulers when inflow is from Markov fluid flow sources. For

simplicity we focused on sources of two classes and formulated scheduling problem to estimate

overflow probability and mean waiting time. We employed the key idea of FIFO queue

discipline and derived a single packet multiplexing system consisting of buffer space and

services capacity. We investigated FIFO, SP, GPS and simulation validation was done with

analytical model or in literature [2], [3] and [5] which yielded high accuracy. The overflow

probability was low with all the schedulers, but lowest for GPS and PRIO high priority class,

meaning that FIFO, SP, and GPS all have potential for efficient network utilization. Therefore,

they can favorably support multi-services network. In particular, the advantages of GPS make it

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a preferable choice. However, SP gives excellent service for the high priority class. GPS

provides flexibility in bandwidth allocation by dynamic weight control. GPS allows for tighter

delay bounds than FIFO and SP since it yields low variability of the packet inter-arrival times of

the output stream. FIFO behaves averagely good but better with balanced load.

This performance analysis results are applicable in enhanced uplink scheduling in multi-services

Code-Division Multiple Access (CDMA) network, to optimally utilize limited capacity in frame

with UMTS standard.

In the future work evaluation of the performance of schedulers in terms of admissible region and

application of the packet schedulers in UMTS/CDMA network, incorporating specific features of

radio channel in the implementation can be consider. A network with a preventive CAC that

relies on feedback, based on the overflow probability and the mean waiting time of congestion in

buffer could be explored. In addition, dynamic GPS weight selection could be included when

developing a proper UMTS standard network.

The following are the summarized conclusive facts and table:

• All the three schedulers are work conserving meaning that the server is never idle when

there is work to be done.

• The FIFO scheduler implements sharing among the call classes.

• The PRIO scheduler implements priority among the call classes.

• The GPS scheduler implements sharing and isolation among the call classes.

• The FIFO and PRIO scheduler provides a long-term fraction of the server capacity to

each class.

• The GPS scheduler provides both a short-term (by isolation) and a long-term fraction of

the server capacity to each class.

• The packet inter-arrival times of a stream changes as the stream passes a multiplexer

(packet scheduler) .

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• The computational complexity of the analytical model for FIFO, GPS and PRIO

increases exponentially with the number of classes.

Table 2. Advantages and Disadvantages of Packet Schedulers.

Packet

Schedulers

Advantages

Disadvantages

FIFO Low overflow probability;

Efficient network utilization.

High inter-arrival time variability.

GPS Priority by weight control,

Low inter-arrival time variability,

Low overflow probability;

Efficient network utilization

Dynamic weight updates are

expensive

PRIO Explicit class priorities,

Low overflow probability;

Efficient network utilization

Large difference between classes,

High inter-arrival time variability

References

[1] Craig Partridge [1994]. “Gigabit Networking” Addison-Wesley. Reading, MA, pp

276.

[2] D. Anick, D. Mitra, M. Sondhi, “Stochastic theory of data handling system with

multiple sources”, Bell System Technical Journal, Vol. 61, No. 8, pp. 1871-1894, Oct

1982.

[3] A. Elwalid and D. Mitra. “Analysis, approximation and admission control of a multi-

service multiplexing system with priorities”, INFOCOM’95, 1995.

[4] S. Jacobsen, L. Dittman, “A fluid flow queueing model for heterogenous on/off

traffic”, RACE BLNT Workshop, Munchen, 1990

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[5] F. Presti, Z. Zhang and D. Towsley, “Bounds, approximations and applications for a

two-queue GPS system”, INFOCOM’96, 1996

[6] E. Altman, “Capacity of multi-service cellular networks with transmission rate

control: a queueing analysis”, In Proc. MOBICOM’02, Sept., Atlanta, GA, USA,

2002

[7] G. Fodor, “Performance analysis of the uplink of a CDMA cell supporting elastic

services”, Submitted, 2005

[8] Ersnt Nordström, “Course compendium in net modelling”, Department of Computer

Science, Dalarna University, Borlänge, Sweden, Nov, 2002 pp 192

[9] C.Chang, C.J. Chang and K.R Lo “Analysis of a hierarchical cellular system with

reneging and dropping for waiting new calls and handoff calls” IEEE trans. Veh.

Technol., vol 48, no.4, pp 1080_1091, 1999

[10] Yuguang Frang and Yizhang “Call Admission Control Schemes and Performance

Analysis in Wireless Mobile Networks.” IEEE trans. Veh. Technol., vol 51, No.2

March 2002

[11] William Stallings. (2002), 2nd Edition, “Wireless Communication & Networks”

upper Saddle River, NJ 07458. ISBN: 0-13-196790-8

[12] D. Mitra, “Stochastic theory of a fluid model of producers and consumers coupled by

a buffer,” Adv. Appl. Prob., vol.20 pp. 646-676, 1988.

[13] A. Elwalid and D. Mitra, Analysis and Design of Rate-Based Con- gestion Control

ofHigh Speed Networks, I:Stochastic Fluid Models, Access Regulation, Queueing

Systems, Vol. 9, 1993, pp. 29-64.

[14] A. K. Parekh and R. G. Gallager, A Generalized Processor Sharing Approach to Flow

Control in Integrated Services Networks: The Single Node Case, IEEE/ACM

Transaction on Networking,Vol. 1, No. 3, pp. 344-357, June 1993.

[15] A. K. Parekh and R. G. Gallager, A Generalized Processor Sharing Approach to Flow

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Control in Integrated Services Networks: The Multiple Node Case, IEEE/ACM

Transaction on Networking, No. 2, Vol. 2, pp. 137-150, April 1994.

[16] L. Kosten, “Stochatic theory of data-handling system with groups of multiple

soucres” Proc. Int. Symp. Perf. Comp. Commun. Syst., IFIP, Zurich, Switzerland,

Mar. 1984

Appendix

Implementation

Overall simulator design

The simulator is based on discrete event simulation using a fluid flow model with continuous

time. The simulation is driven by discrete events (the burst arrival/departure event represents the

start/end of a burst). The foundation of the simulation is the event list, which is a linked list (data

structure) of event records. Each event has a continuous time entry when the event should occur.

The event list is sorted by the event occurrence times, in increasing order. The head of the event

list contains the next event that should happen. When the current event is processed by the

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simulator, some other events that are incurred by the current event may be inserted in the event

list.

The time when the event should occur, or time between events, is determined by the Inverse

method using a random number generator. A random number with distribution F(x) is

determined by F-1

(U) where U is a uniform random number in the interval [0,1].

Determine time to next event according to exponential distribution .

Arrival_process is MARKOV and event_type is BURST_ARRIVAL and

BURST_DEPARTURE events.

The computation of buffer overflow statistics function for the three types of burst event

analysis is listed below:

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gps_burst_event_analysis()

static void gps_burst_event_analysis(double x_buffer_state[K],

int x_burst_state[K],

double t_y_event,

double t_x_event,

double total_sat_time[K],

double lost_fluid[K],

double queue_len[K],

int n_burst_event)

int j;

int x_congested[K];

int empty[K];

double in_flow[K], out_flow[K];

double y_buffer_state[K];

double packet_count;

double sat_packet_count;

double free_buffer_size[K];

double sat_time;

double net_flow[K];

double interval;

double t_y_sat_time;

for (j=0; j<K; j++)

queue_len[j]=(n_burst_event*queue_len[j]+x_buffer_state_gps[j])/

(n_burst_event+1);

for (j=0; j<K; j++)

in_flow[j]= x_burst_state[j]*call_class[j].peak;

if (x_buffer_state_gps[j]>0.0) empty[j]=TRUE;

else empty[j]=FALSE;

for (j=0; j<K; j++)

out_flow[j]=call_class[j].phi*trunk_system.capacity;

out_flow[j] +=

max(call_class[1-j].phi*trunk_system.capacity-in_flow[1-j],0.0)*

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empty[1-j];

net_flow[j] = fabs(in_flow[j]-out_flow[j]);

if (in_flow[j] <= out_flow[j])

x_congested[j]=FALSE;

else

x_congested[j]=TRUE;

for (j=0; j<K; j++)

interval = t_y_event-t_x_event;

if (x_congested[j]==TRUE) /* Congested */

packet_count=net_flow[j]*interval;

total_bufferless_sat_time[j] += interval;

y_buffer_state[j] = min(x_buffer_state[j], packet_count,buffer_size_mbit[j]);

free_buffer_size[j]=buffer_size_mbit[j]-x_buffer_state_gps[j];

if (packet_count>=free_buffer_size[j])

t_y_sat_time = t_x_event+(free_buffer_size/net_flow[j]);

sat_time=t_y_event-t_y_sat_time;

sat_packet_count=net_flow[j]*sat_time;

total_sat_time[j] += sat_time;

lost_fluid[j]+=sat_packet_count;

if (x_congested[j]==FALSE) /* Not congested */


y_buffer_state[j] = max(x_buffer_state[j]-packet_count,0.0);

x_buffer_state[j] = y_buffer_state[j];

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prio_burst_event_analysis()

static void prio_burst_event_analysis(double x_buffer_state[K],


double t_y_event,

double t_x_event_prio,

double total_sat_time[K],

double lost_fluid[K],

double queue_len[K],

int n_burst_event)

int j;

int x_congested[K];

int empty[K];






double sat_time;

double net_flow[K];

double interval;


for (j=0; j<K; j++)

queue_len[j]=(n_burst_event*queue_len[j]+x_buffer_state_prio[j])/

(n_burst_event+1);

for (j=0; j<K; j++)

in_flow[j]=x_burst_state[j]*call_class[j].peak;

/* This class has high priority */

out_flow[0]=trunk_system.capacity;

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/* This class has low priority */

if (in_flow[0] < trunk_system.capacity)

out_flow_tilde[0] = in_flow[0];

else

out_flow_tilde[0] = trunk_system.capacity;

out_flow[1]=trunk_system.capacity-out_flow_tilde[0];

for (j=0; j<K; j++)

net_flow[j]=fabs(in_flow[j]-out_flow[j]);

if (in_flow[j]<=out_flow[j])

x_congested[j]=FALSE;

else

x_congested[j]=TRUE;

for (j=0; j<K; j++)

interval = t_y_event-t_x_event;

if (x_congested[j]==TRUE) /* Congested */


y_buffer_state[j] = min(x_buffer_state[j]+

packet_count,buffer_size_mbit[j]);

free_buffer_size=buffer_size_mbit[j]-x_buffer_state_prio[j];

if (packet_count>=free_buffer_size)

t_y_sat_time = t_x_event_prio+free_ buffer_size/net_flow[j];

sat_time=t_y_event-t_y_sat_time;

total_sat_time[j] += sat_time;

sat_packet_count=net_flow[j]*sat_time;

lost_fluid[j] +=sat_packet_count;

if (x_congested[j]==FALSE) /* Not congested */


y_buffer_state[j] =max(x_buffer_state_prio[j]-packet_count,0.0);

x_buffer_state[j] = y_buffer_state[j];

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fifo_burst_event_analysis()

static void fifo_burst_event_analysis(double *x_buffer_state,


double t_y_event,

double t_x_event,

double *total_sat_time_fifo,

double *lost_fluid_fifo,

double *queue_len_fifo,

int n_burst_event)

int j;

int x_congested[K];

int empty[K];






double sat_time;

double net_flow[K];

double interval;


*queue_len_fifo=(n_burst_event*(*queue_len_fifo)+(*x_buffer_state_fifo))/

(n_burst_event+1);

in_flow_total=0;

for (j=0; j<K; j++) in_flow_total += x_burst_state[j]*call_class[j].peak;

if (in_flow_total <= trunk_system.capacity)

x_congested=FALSE;

else

x_congested=TRUE;

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net_flow = fabs(in_flow_total-trunk_system.capacity);

interval = t_y_event-t_x_event_fifo;

y_buffer_state=0;

if (x_congested==TRUE)

packet_count=net_flow*interval;

y_buffer_state = min(*x_buffer_state_fifo+packet_count,

buffer_size_mbit_fifo);

free_buffer_size=buffer_size_mbit_fifo-*x_buffer_state_fifo;

if (packet_count>=free_buffer_size)

t_y_sat_time = t_x_event+free_buffer_size/net_flow;

sat_time = t_y_event+t_y_sat_time;

sat_packet_count=net_flow*sat_time;

*total_sat_time_fifo += sat_time;

*lost_fluid_fifo +=sat_packet_count;

if (x_congested==FALSE)

packet_count=net_flow*interval;

y_buffer_state = max(*x_buffer_state_fifo-packet_count,0.0);

*x_buffer_state_fifo = y_buffer_state;

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