Performance of multiple-access schemes for data communication

Performance of multiple- access schemes for data

communication Mushfiqur Rahman and Rana Ejaz Ahmed propose three new hybrid schemes

for dealing with collision resolution

The problem of collision resolution in multiple-access packet communication systems is investigated. Several hybrid schemes, which combine both random and reservation access strategies, are proposed. Delay analysis is performed by modelling the source buffer as an M/C/I queue, and results are verified by simulation. Both analysis and simulation indicate that the proposed systems are stable and adapt dynamically between a pure slotted Aloha mode for low traffic and TDMA for high traffic.

Keywords: computer networks, packet communication, collision resolution, multiple-access, network performance, TDMA, Aloha

In packet broadcasting networks, a large number of geographically distributed data users are interconnected via a broadcast channel. Examples of a broadcast channel are satellite, ground radio and coaxial cable. A multiple access scheme is needed to allocate the channel capacity appropriately among the users in order to achieve efficient utilization of expensive channel time and to provide a high degree of connectivity for communication among users.

Many multiple-access schemes have been proposed and implemented. Fixed assignment techniques consist of allocating the channel to the users, independently of their activity, by partitioning the time/bandwidth space into slots, which are assigned in a static predetermined fashion. Examples are frequency division multiple access

Department of Electrical Engineering, University of Petroleum & Minerals, Dhahran, Saudi Arabia

0140-3664/86/050241-09 $03.00 ©

(FDMA) and time-division multiple access (TDMA). It has been established that TDMA is superior to FDMA in many practical cases 1. These techniques are efficient only if the message traffic is steady. In computer communication, however, traffic is bursty, low duty cycle with a high ratio of peak-to-average traffic intensity, and for this kind of traffic, fixed assignment techniques are inefficient. In random- access schemes, the entire bandwidth is available to the users as a single channel to be accessed randomly. Examples are Aloha, slotted Aloha, and the tree algorithm 2-4. These schemes have low maximum achiev- able throughput (e.g. 1/e in the case of slotted Aloha).

Slotted Aloha is efficient at low values of throughput while the performance of TDMA is better when throughput is high. In the proposed schemes, hybrid schemes having both random access and reservation slots will be considered.

In this paper, channel and source models used in the proposed multiple-access schemes will be presented. A dynamic scheme (Scheme A) is presented, which involves dynamic allocation of slotted Aloha and TDMA slots, ~while a dynamic scheme (Scheme B), which involves dynamic allocation of S-Aloha and reserved slots, is also analysed. Another dynamic scheme (Scheme C) is then discussed.

Analytical results of the various schemes were verified by simulation studies. Each simulation run consisted of 50 000 or more time slots. During this time, messages were generated at each end user according to the assumed arrival statistics. Subsequent to the generation of a message, a complete time record was maintained regarding its transmission, collision, storage and retransmission. The individual records were later compiled to calculate the desired performance measures.

1986 Butterworth & Co (Publishers) Ltd

vol 9 no 5 october 1986 241

The following notation will be used:

N: number of identical users R: round trip propagation delay (slots) ~: slot width in seconds Ps: prob. [system in S-Aloha mode] Pt: prob. [a user transmits a newly generated packet in a slot] E(D): average delay of an accepted packet in seconds

CHANNEL AND SOURCE MODELS

Channel model

The broadcast channel is assumed to be time-slotted; that is, the channel time is divided into equal segments called slots. Let the slot length be =, and in all schemes considered, = = 20 ms. These slots are long enough that exactly one packet can be transmitted in a given slot. The channel is to be shared by N sources. These sources are assumed to be synchronized to slot boundaries.

In schemes B and C only, each time slot is further divided into two main parts. One part, of length =1, is for actual message transmission and the other part, of length =2 = • - =1, is further divided into N minislots. This situation is shown in Figure 1. One minislot is assigned to each user. When a user transmits a packet in a slot, he puts a '1' in his assigned slot, otherwise he puts a '0'.

Each source can listen to the transmission of packets from all the sources, including itself. A slot is said to be empty if no packet is transmitted in it by any source. If only one source transmits a packet in a slot, the transmission is regarded as successful. If two or more sources transmit packets in the same slot, a collision occurs and none of the packets can be received correctly. Each user has the ability to distinguish if a previously received slot was empty or whether it was a successful transmission or a collision.

Poisson source model

Single packet messages are assumed to be arriving at the sources that share the channel. All N sources are assumed to be alike. Each source generates k packets/s, where k is a poisson random variable with mean ~.. Two buffers are available at each source; one is used to store newly generated packets and the other to store collided packets.

11121 1 ~'2 T1

Figure 1. Slot subdivision in Schemes B and C

we reserve a slot for each of N users upon detecting a collision. The channel can be in one of the two states:

• State 1 (slotted Aloha). The users transmit in a slot whenever they have packets ready to transmit.

• State 2 (TDMA mode). A slot is reserved for every source connected to a channel. If a source has a colliding packet waiting to be retransmitted, it transmits in its assigned slot; otherwise it may transmit any waiting, newly generated packet in its assigned slot. Each user maintains a reservation table (RT) which identifies the reserved slots and their assigned users. The RT is updated at each user whenever a collision is detected.

Scheme Aworks as follows. The channel remains in state 1 until a collision is detected. Upon detecting a collision, the RT at each user is updated, and the system goes to state 2. After spending N slots in state 2, the system returns to state 1.

Figure 2 shows a possible collision where there are four users and where the propagation delay is 0 and 3. The most attractive feature of this scheme is that, at any time, the maximum number of collided packets at a source is the integer part of (R + 1).

Figure 3 shows the delay-throughput curves for scheme A for N = 10 and N = 100, where R= = 0.27 s (satellite channel). The maximum throughput may reach unity at the expense of a large average delay.

Delay analysis - - Scheme A

It is assumed that two buffers at each user are of infinite length. Let P0 be the probability that the retransmission buffer is empty at the beginning of a reservation frame. The detailed delay analysis is performed in Reference 5, and the results are verified by simulation. Here, the delay analysis of scheme A is summarized briefly. The total

I Ix1,12131,1 I Ix1,12131,1 I I a Time

SCHEME "A"

Every user is able to detect a collision. Whenever a collision is detected, collided packets are queued in the retransmission buffer of each collided user, but all N users do not know the identity of all collided users. In the worst case, all N users may be involved in a collision. Therefore,

Ixl Ixl 1112131,1112131,1111 b Time ='

Figure 2. Typical epoch developed in Scheme A coll ision when (a) N = 4, R = O, (b) N = 4, R = 3 CX" denotes a coll ision in that slot)

242 computer communications

8.40

7.00

5.60

4 .20 t -

8

2.80

1.40

0 . 0 0 ~ 0.00 0.20 0.40 0.60 0.80 1.00

Throughput (S)

Figure 3. Delay-throughput performance for Scheme A when R~ = 0.27s; • N = 10, • N = 100

average delay suffered by a packet has several com- ponents and can be expressed as:

N ~ "~ E(D) = E(T) + P c - - - + -

2 2

where E(T) is the average delay of a newly generated packet, and the other two terms account for the collision and time slotting of the channel. E(T) is calculated by modelling the buffer behaviour at a user as an M/G/I queue 6. Thus

E(T) = E ( W ) +

where E(W) is the average waiting time in the transmission queue and ~ is the average service time for a newly generated packet. Using well known results of M/G/I queues, E(T) can be expressed as:

XE(x 2) E(T) = - - ~

2(1 - p)

where

p A ~

The final expression for total average delay is obtained by combining these results s and is given by

E ( D ) - 2(1 - p ) t - E + p c R ~ + - - + R z + 2 (1)

where

k' = k - (1 - Ps)PoX

p c = l (1 X"~/N- 1 - - ( 2 )

Ps /

= (1 - p'c)$ + p'c(N + 1)~

E(x 2) = (1 - pc):2 + p'c(N + 1)2z2

and p = ~

All the terms on the right-hand side of equation (2) are either given or may be obtained analytically, except forps which is obtained by solving the following equation:

p(s-Aloha mode) + p(TDMA mode) = 1

The above equation turns out to be a transcendental equation in Ps and thus numerical methods were used to solve for Ps (see Reference 5).

Figures 4 and 5 compare the simulation and analytical results and indicate good agreement between the two.

S C H E M E B

In this scheme, the reservation for collided users only is made on collision detection. The system can be in one of two states:

• State I (slotted Aloha). The users transmit in a slot whenever they have packets ready to send, and they

4 .80

4.00 -

~, 3.20

.~ 2.40 -- I

1.60 - -

. . /

0.00 0.00 0.20 0.40 0.60 0.80 1 .O0

Traf f ic intensity

Figure 4. Comparison between analytical and simulated delay for Scheme A for N = 10 and Rz = O.Os; simulation, analytical


4.80

4.00

3.20

-~ 2.40 c

=E

1.60

0.80

0.00 / 0.00

f

Figure 5. delay for Scheme A where N = 10, R~ = 0.27s; simulation, analytical

0.20 0.40 0.60 0.80 1.00

Traffic intensity

Comparison between analytical and simulated

also give their own identification by sending signals in assigned minislots.

• State 2 (reserved mode). A slot is reserved for a user to retransmit a previously collided packet. Each user maintains an RT, which identifies the reserved slots and their assigned users. The RT is updated at each user whenever a collision is detected.

Scheme B works as follows. The channel remains in state 1 until a collision is detected. Upon detecting a collision, the RT at each user is updated, and the system goes to state 2. Let the users be labelled 1, 2, . . , N. Slots are reserved for collided users with the highest priority to user 1 and the lowest to user N (i.e. user I has higher priority over 2, and so on). After resolving all collisions, the system returns to state 1. Figure 6 shows a typical epoch developed when there is a collision for N = 4 and R = 3. In this scheme, there are at most [R] t collided packets at a user's retransmission buffer (where [R] t is the integer part of (R + 1)).

D e l a y a n a l y s i s - - s c h e m e B

It is assumed that the two buffers at each user are of infinite length. First, a procedure is outlined for finding Ps in this scheme for channels with R = 0.

A packet which has had a collision and is waiting for retransmission is said to be backlogged, and the user that

Ixl M 1'121313141111111 Time ==

Figure 6. Typical epoch developed on a collision when N = 4 and R = 3 in Scheme B (9(" denotes a collision among users 1, 2 and 3 and "XX" denotes a collision between users 3 and 4)

has such a packet in its retransmission buffer is also termed backlogged (or in retransmission mode). For R = 0, no newly generated packet is transmitted until the collision is resolved, so each user can have, at most, one backlogged packet. The channel can be viewed as a discrete time system with (N + 1) possible states, corresponding to the number Xn of users in the retransmission mode at the beginning of the nth slot (n = 1, 2 . . . . ). The sequence of system states forms a discrete time Markov chain X = {Xn; n > 0} with state-transition matrix P = {Pii} where

Pii = P[Xn + 1 = i lXn = i]

and where

i , j ~ {0, 1, 2 , . . N }

Once the system is at state k (k > 0), the state cannot increase during any subsequent slots until the system returns to state O. Decreases in state are always in units of one, since the number of users in retransmission mode can be reduced by one during a single slot. The transition from 0 to 1 is impossible because it will always yield successful transmission.

When the system is in S-Aloha mode continuously, the system capacity is 1/~ packets/s and a user transmits a newly generated packet in a slot with probability p = ~.~ (see Reference 7). When Ps < 1, the effective capacity is psl/~, and the probability with which a user transmits a newly generated packet in a slot is

Pt = - - (3) Ps

The transition probabilities are:

Pi, i - 1 = 1, i=/=O

P00 = (1 - pt) N + Npt(1 - pt) N - 1

Poi = (N)P/(1 -- Pt )N - i , j > 2

Pii = O, otherwise

Thus we can construct P = {Pii}, which is an (N + 1) X (N + 1) matrix. Then:

n = n . P (4)

where I I = [No ]]1 .. I-IN] is a vector of equilibrium state probabilities and where

I I i = Lim P[X n = I1 (5) n .-~cO

Clearly

Ps = IIo (6)


The (N + 1) equations in expression (4) are transcendental in Ho, and numerical techniques are applied to solve fo r ] ] along with the condition

N

~ = 1 (7)

k = 0

An expression will first be found for E(D) for channels with R = 0. The average delay of a newly generated packet is

E(T) = E(W) + ~ (8)

where E(W) is the average waiting time, and 7 is the average service time for a newly generated packet. The service time is • in S-Aloha mode. To find the average service time in the reserved mode, it is necessary first to establish the average number of collided packets resulting from a collision in an S-Aloha slot. Let this number be j. Then:

P[/ arrivals in an S-Aloha slot] = ps(/N)pt/(1 -- pt) N - j

and

p[of a collision event] = p511 - (1 - p t ) N - NPt(1 - pt) N - l ]

The probability of j arrivals, given that a collision has taken place, is

(/N)p{/(1 -- pt)N - i P[j/ /> 2] -

1 - ( 1 - p t ) N-NPt(1 - p t ) N-1

= p/.(say)

Therefore: N

~= T i p i (9) i = 2

Thus, in the reserved mode, service time is (~ + j~), and the average service time is

= (1 - pc)~ + PcO: + j-l:) (10)

where Pc is the probability of a collision at the time of servicing a packet from the main transmission queue. Thus, Pc is simply the probability of one or more transmissions from the remaining (N - 1) users. So:

p c = l - 1 - Ps

and

e(x 2) = (1 _,)~2 - ~c + p;:(.,: + ~ ) 2

(11)

(12)

Modell ing the main buffer behaviour at a user as an M/G/ I queue,

E(x 2) E(T) - I- ~ + - (13)

2 " I - p 2

where p = X~7 and the term ~/2 on the right-hand side accounts for time slotting of the channel.

In addition, each collided packet has a delay of

(=~L~2 ~ . Hence

For R > O, a packet needs at least R~ to be transmitted through the channel, and each collided packet also has to wait for R slots before the reservation mode starts. Thus

E(D)IR > 0 = E(D)IR = 0 + R~ + p'~(R=) (1 S)

Simulation and analytical results are compared for N = I0 where R~ = 0 (Figure 7) and where R~ = 0.27 (Figure 8).

For R > 0, the same probability density function is used for service time, which is somewhat inaccurate, particularly for high values of traffic intensity. Hence, there is some discrepancy between analytical and simulation results for high traffic intensities.

Scheme B changes adaptively from pure S-Aloha in low traffic to reserved mode in high traffic. Significantly, for a wide range of throughput, system performance does not degrade with an increase in the number of users. However, the actual throughput decreases as N increases because of greater overhead in each packet.

B u f f e r b e h a v i o u r - - S c h e m e B

It has been assumed that there are infinite buffers in the delay analysis for scheme B. However, in practice, each

4.80

4.00

3.20

d

> . ¢o

-6 2 . 4 0 -

1.60 - -

0.80 --

0.0C 0.00

Figure 7. de/ayforScheme B; N = 10, RT, = 0 s;

analytical

I

i . . ! -J - : ~ , - - , ~ ' I I I 0.20 0.40 0.60 0.80 .00

Traffic intensity

Comparison between simulated and analytical simulation,


4.80

4.00-

3.20 --

>.

-~ 2 . 4 0 - c

1.60 --

0.80 --

0.00 0.0

Figure 8. delay for Scheme B; N = 10, simulation, analytical

i

I

i

.,// ~ J I I I I I I I I I

0.20 0.40 0.60 0.80 1.00

Traffic intensity

Comparison between simulated and analytical R~ = 0 . 2 7 s ;

user maintains two finite-length buffers. The first (main) buffer of length L packets is used to store newly arriving packets. The second (retransmission) buffer is used to store collided packets. We are interested in the design of the main buffer for various traffic intensities for a specified overflow probability (Pot).

As all users are identical, the buffering calculation must be concentrated at only one user. The length of the retransmission buffer at each user is assumed to be [R] t packets (where [R] t is the integer part of (R + 1), as there may be at most [R] t collided packets requeued to this buffer. The retransmission buffer will have zero overflow probability. The buffers at a user can be modelled as shown in Figure 9. In normal operation, switch S is at position 1, and S-Aloha mode (state 1) is used until a collision is detected. Upon detecting a collision, S moves to position 0, and it will remain at this position until all collided packets resulting from previous slots from all users are retransmitted. The Kekre and Saxena approach s for buffer behaviour with server interruption is directly applied to calculate buffer overflow probabilities. The

pN:=ly:rriving I

C°:l~dt sed t Figure 9.

Main buffer length = L

R etransmission buffer

'1' Switch 'S' ,"-~, ~Server ~_ (Slotted channel)

Buffering at a source

approach as outlined in the original paper consists of obtaining a set of steady-state buffer size probabilities in terms of the poisson arrival rate, steady-state probabilities of the switch in states I and 0, etc. In particular, Psi used in Reference 8 is given by

Psi = P[switch is at 1]

= Ps (16)

where Ps is given by equation (6). Pot for various total traffic intensities as a function of/_ are plotted in Figure 10 for N = 10. These results are also verified by long simulation runs. The analytical calculations for Pot were made on computer. Owing to finite word length, the co- efficient < 10 - is was set equal to zero.

A small buffer length (L ~ 10) is needed to achieve very low overflow probability.

S C H E M E C

When the system is in the reservation mode of scheme B, all users know that a particular future slot is reserved for a particular user. So, in this mode, there is no need to send identification signals in minislots. Instead, a user can give its main queue length information in those minislots.

O O

J~ 2

1.00 4.00 7.00 10.00 13.00

Buffer length

16.00

Figure 10. Pof as a function of main buffer length for Scheme B for various traffic intensities when N = 10; (a) p = 0.01, (b) p = 0.3, (c) p = 0.5, (d) p = 0.7, (e) p = 0.9


Working of scheme C

The channel and source models for this scheme are the same as those of Scheme B, except that a user can also send its queue length (of main buffer with newly arriving packets at its input) information in minislots.

The system can be in one of three states:

• State 1 (slotted Aloha). Users transmit in a slot whenever they have packets ready to send, and they also give their own identification by sending signals in their assigned minislots.

• State 2 (reserved mode 1). A slot is reserved for a user for retransmit a previously collided packet and that particular user gives its queue length information of main buffer in minislots (excludingthe packet currently being transmitted).

• State 3 (reserved mode II). When queue length information is detected, r slots are reserved for a user if he reports his queue length to be equal to r.

Each user maintains an RT and a queue length table (QLT) for all users connected to the channel. The RT identifies the reserved slots and their assigned users. The RT and QLT are updated and modified upon collision detection, collision resolution and executing state 3. Scheme C works as follows.

The system remains in state 1 until a collision is detected; the system then goes to state 2, and collisions are resolved, just as in state 2 of Scheme B. The RT and QLT at each user are updated. (Once a user reports its queue length, it will not attempt transmission on slotted Aloha slots, thus decreasing the probability of collision for other users until all its reported packets are transmitted on reserved mode II slots). Upon detecting a reported queue length of a user, the system switches to state 3. After transmitting reported packets in state 3, the system will switch to state 1 or 2, depending upon any collided packets waiting to be retransmitted at any source.

States 2 and 3 can be viewed as a single state, namely the reservation state. However, there is a clear subdivision of this state: in state 2 only previously collided packets are transmitted while state 3 caters for fresh packets only, for which reservations were made through the reporting of queue length in state 2.

Figure 11 shows a typical situation upon detecting a collision when N = 4 and R = 3."

I x l l l 1112131 I'1 13131111 Time

Q u e u e l e n g t h t a b l e

U s e r Q u e u e length

1 1

2 0

3 2

4 0

Figure 11. Example of collision being detected in Scheme C when N = 4, R = 3 (~X'denotes a collision between users 1, 2 and 3)

Delay-throughput performance where N = 10 and N = 100 forR= = 0.27 s is ~iven in Figure 12.As in scheme B, there are, at most, [R] T collided packets at a user's retransmission buffer. The delay-throughput performance has improved significantly; however, this has been achieved at the expense of greater system complexity. The system is stable and is immune to the number of users over a wide range of throughput.

Delay analysis - - Scheme C

The exact delay analysis for Scheme C becomes very complicated owing to correlated total input traffic and a decision process at a slot while the system is in states 2 and 3. An approximate analysis is presented here for R~0 channels only. One major difficulty airses when one tries to find an analytical expression for Ps. An important result that can be deduced from the simulation study of multiple access Scheme C is that ps is almost independent of the number of users (N) and it depends only on Pt. These results are tabulated in Table 1, the simulation run was 50 000 slots for a particular Pt.

As Ps is a function of Pt only, data in Table can be approximated by means of a least-square curve-fitting method using an nth degree polynomial in Pt. If n = 4:

Ps = 1.005 - 0.1937pt+ 0.5632p 2- 3.569pt3+ 2.203pt 4 (17)

The mean square error is 8.8 X 10 -6. Equation (17) gives an empirical relation for Ps.

Let the total traffic (newly generated plus collided packets) form an independent poisson process with mean

3.60

r -

3.00

2.40

1.80

1.20

0.60

0.00 I I I I t I i i t

0.00 0.20 0.40 0.60 0.80 1.00

Throughput (S)

Figure 72. Delay throughput curves for Scheme C when R~=O.27s ; •N=10 , • N = 1 0 0


Table 1. Simulation results for Ps in Scheme C for R = O

Total traffic intensity Pt

Prob.[system in S-Aloha mode]

N = 1 0 N = 2 0 N =100

0.01 0.999 96 0.999 96 0.999 990 0.04 0.998 76 0.998 48 0.998 799 0.10 0.991 54 0.991 14 0.990470 0.20 0.964 66 0.962 68 0.960 930 0.30 0.915 40 0.914 38 0.906 000 0.40 0.841 78 0.838 40 0.831 800 0.50 0.743 90 0.737 32 0.727 900 0.70 0.452 64 0.439 46 0.436 300 0.90 0.126 70 0.125 54 0.128 560 1.00 0.010 72 0.013 58 0.107 870

N24, and, further, let p' be the corresponding traffic intensity (p' = N~; ~). Then:

N;~' = N;k + Ps. P[collisionlS-Aloha mode] N;k

= N ~ , + Ps. Pc. N ~ ,

Therefore

p' = I~[1 + PsPc]

where Pc is

Pc = pk 1 -- Pt =

(18)

The queueing system can now be modelled as an M/D/1 queue, where the input traffic intensity is p' and the standard delay result 6 is used:

(p,)2 p' +

2(1 - p') E(D) = + - (19)

N~ 2

The comparisons between simulated and analytical results are plotted in Figure 13 for R = 0. The close agreement of results (especially for Pt < 0.8) suggests that Scheme C behaves like a perfect scheduling algorithm (M/D/1 queueing system) with the modified value of intensity p' given by equation (18).

1.20

1.00

0.80

-~ 0.60 C

0.40

! I i ! I I I

/ 0.20

0 . 0 0 ~ 0.00 0.20 0.40 0.60 0.80 1.00

Traffic intensity

Figure 13. Comparison between simulation and analytical results for Scheme C when R = O, N = 10; simulation, analytical

Delay - - th roughput tradeoffs

In all proposed schemes, the maximum throughput may approach unity, and all schemes adapt dynamically and smoothly to traffic variations. At low traffic, the schemes behave like S-Aloha, while at high traffic intensities they tend to dynamic assignment techniques.

Scheme B offers better delay-throughput tradeoffs than Scheme A, because in the latter case, a slot is reserved for each user on detecting a collision and some of these slots may be unused; this results in a decrease in throughput and an increase in the average delay. Scheme C offers the best delay-throughput tradeoffs owing to the efficient utilization of slots. But the major drawback is the complexity of implementation. Figure 14 shows a comparison of all the proposed schemes, S-Aloha and TDMA for N = 100. It is evident that the proposed schemes offer better performance than S-Aloha or TDMA.

D I S C U S S I O N S A N D C O M P A R I S O N S

Stabi l i ty

All proposed multiple access schemes are stable. This is due to the fact that a packet collides, at most, once before it is received successfully.

C O N C L U S I O N S

Three multiple-access schemes for packet communications over broadcast channels have been proposed. These schemes are studied under two different channel environments: ground radio (or LAN) and satellite. Random schemes (e.g. slotted Aloha and tree algorithm) are efficient at low throughput, while the performance of fixed assignment TDMA is betterwhen throughput is high.


210.0

180.0

150.0

A

O

120.0

f -

=E 90.0

TDMA

S-ALOHA A sending queue length information of each collided user, hence reserving more slots for that user in order to avoid further collisions. Schemes B and C are just S-Aloha at low traffic and behave as a near-perfect scheduling algorithm (M/D/d) at high traffic intensities.

The most interesting feature of all the proposed schemes is their stability. This is due to the fact that a packet suffers, at most, one collision before it is received successfully. The maximum throughput in each scheme can approach unity (if overhead is neglected). Delay analyses are performed for all schemes and are verified by simulation. Buffer analyses show that a user needs a buffer of small lengths (L - 10) in order to reduce the probability of overflow.

The multiple access techniques discussed in this paper have possible applications in packet radio and satellite communications. The underlying concepts are also applicable in the rapidly growing field of local area networks.

60.0

30.0

0 . 0 ~ 0.0 0.2 0.4 0.6 0.8 1.0

Throughput

Figure 14. Comparison curves for proposed schemes A, B and C, S-Aloha and TDMA

Random access may be combined with TDMA in order to achieve better delay-throughput characteristics for the whole range of traffic intensity. Under Scheme A, the reservation decisions are made only on collision detection; otherwise the system remains in S-Aloha mode. This scheme adapts from S-Aloha at low traffic intensities to TDMA at high intensities. Scheme B is a more complex one and requires a small overhead in each packet for the purpose of user identification, thus reserving slots for collided users on each collision. Scheme C is just an extension of Scheme B with the additional capability of

R E F E R E N C E S

1 Rubin, I 'Message delays in FDMA and TDMA communication channel' IEEE Trans. Commun. Vol 27 No 5 (May 1979) pp 769-777

2 Tobagi, F A 'Multiaccess protocols in packet communication systems' IEEE Trans. Commun. Vol COM- 28 No 4 (April 1980) pp 468-488

3 Abramson, N 'The Aloha system - - another altemative for computer communication' Proc. 1970 Fall Joint Computer Conf. AFIPS Vol 37 pp 281-285

4 Capetanekis, J I 'Tree algorithm for packet broadcast channels' IEEE Trans. Inf. Theory Vol IT-25 No 5 (September 1975) pp 505-515

5 Ahmed, R E Multiple access schemes for data communications M S Thesis, Univ. of Petroleum & Minerals, Saudi Arabia (May 1985)

6 Kleinrock, L Queueing systems Vol I John Wiley, USA (1975)

7 Carleial, A B and l-legman, M E 'Bistable behaviour of Aloha type systems' IEEE Trans. Commun. Vol COM- 23 No 4 (April 1975)

8 Kekre, H B and Saxena, C L 'Finite buffer behaviour with Poisson arrivals and random server interruption' IEEE Trans. Commun. Vol COM-26 No 4 (April 1978) pp 470-474


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Performance of multiple-access schemes for data communication