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Call Admission Control for Multimedia Services in Mobile Cellular Networks: A Markov Decision Approach

Jihyuk Choi; Taekyoung Kwon; Yanghee Choi; Naghshineh, M,

Computers and Communications, 2000. Proceedings. ISCC 2000. Fifth IEEE Symposium

on 3-6 July 2000 Page(s):594 - 599

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Outline

Introduction Model Description SMDP Approach in Our CAC Numerical Results Conclusion

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Introduction There is a growing interest in deploying multimedia

services in mobile cellular networks (MCN) Call admission control (CAC) is a key factor in qualit

y of service (QoS) provisioning for these services Connection-level QoS in MCN is expressed in terms

of Call blocking probability Call dropping probability: is handoff dropping proba

bility The goal of this paper is to find out optimal CAC for

maximize the revenue semi-Markov decision process is employed to m

odel the cellular system

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Model Description We model a one-dimensional cellular network and

describe how to find out optimal admission decisions

Suppose that there are K classes of calls in an MCN (mobile cellular networks)

Call requests of class-i (i = 1,2, ..., K) in cell-n (n =1,2, ..., N) are assumed to form a Poisson process with mean arrival rate λn,i

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Model Description (cont’d) The call holding time (CHT) of a class-i call is a

ssumed to follow an exponential distribution with mean l/μi The rate of class-i calls that depart from a cell due

to service completion is denoted by μi

The number of channels required to accommodate the call, is denoted by bi

The revenue for each on-going class-i call is accrued at rate ri

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Model Description (cont’d)

The following simple model is a mobile terminal (MT) moves through the whole cellular system

The cell residence time (CRT), i.e., the amount of time that an MT stays in a cell before handoff, with mean l/η η represents the handoff rate

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Model Description (cont’d)

In our 1-D cellular network, the probability that an MT will handoff to one of its adjacent cells is 0.5 The rate that a call in a given cell will handoff to

one of its adjacent cells is η /2 The total bandwidth in each cell is the same

and denoted by C The rate of class-i calls that handoff to our s

ystem from outside is denoted by hn,i (n = 1 or N)

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Model Description (cont’d)

The current state of our cellular system is represented by the vector:

where xn,i denotes the number of class-i calls in cell-n

The set Λ of all possible states is given by

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SMDP Approach in Our CAC

The original semi-Markov decision process (SMDP) model considers a dynamic system

It is observed and classified into one of several possible states at random points in time

The SMDP state of the system at a decision epoch is given by the vector s = (x, e)

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SMDP Approach in Our CAC (cont’d) The variable e represents the event type of a

n arrival and is given by

When i <= K the an,i (an,i {0, 1})denotes the origination of a cla

ss-i call within the cell-n When i >=K+1

it denotes the arrival (event) of a class-i call due to handoff from adjacent cells

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SMDP Approach in Our CAC (cont’d)

The action space B can be expressed by

For example, when N = 2, K = 2 and

The action space is actually a state dependent subset of B denoted by

en,i is a vector of zeros, except for an one in the (n*(k-1)+i)-th position

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SMDP Approach in Our CAC (cont’d)

If the system is in state x Λ and the action a Bx is chosen

The expected time (sojourn time), (x, a), until a new state is entered is given by

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SMDP Approach in Our CAC (cont’d)

The transition probability Pxay from the state x to any next state y Λ with action a takes one of the expressions in Table 1

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SMDP Approach in Our CAC (cont’d)

Let r(X, a) be the revenue rate when the cell is in state x and action a has been chosen

If ri is the revenue rate of class-i call, then the total revenue rate for the cell is calculated by

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SMDP Approach in Our CAC (cont’d)

The decision variable zxa, represents the system is in state x and action a is taken

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Numerical Results

For numerical results, we simulated one-cell model (N = 1) and two-cell model (N = 2)

We compare our SMDP CAC with the upper limit (UL) CAC policy that has a threshold ti for a class-i call originating in a cell

The UL policy with threshold (2,l) blocks a new class-1 call originating in a cell if there are already at least two class-1 calls in the cell

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Numerical Results (cont’d)

We let C = 5, K = 2, b1 = 1, b2 = 2 , D1 = 0.02 and D2=0.04

Simulations are carried out as the Erlang load (λn,i/ μi) of every class increases

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Numerical Results (cont’d)

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Numerical Results (cont’d)

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Numerical Results (cont’d)

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Numerical Results (cont’d)

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Numerical Results (cont’d)

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Numerical Results (cont’d)