Average Packet Delay in Random Multiple Access for Satellite Systems

Transcription

1 Average Packet Delay in Random Multiple Access for Satellite Systems MARIO REYES-AYALA 1, EDGAR ALEJANDRO ANDRADE-GONZALEZ 1, JOSÉ ALFREDO TIRADO-MÉNDEZ 1, HILDEBERTO JARDÓN AGUILAR 2 1 Electronics Department Metropolitan Autonomous University San Pablo 180, Col. Reynosa Tamaulipas, Azcapotzalco, ZIP Code 02200, Mexico City MEXICO 2 Section of Communications CINVESTAV-IPN Av. IPN 2508, Col. San Pedro Zacatenco, Zip Code Mexico City MEXICO Abstract: - In this paper, the Random Multiple Access is evaluated for digital satellite system where packet transmission is used. The main parameters to analyze the system are the throughput, the average number of retransmission and the average packet delay. Key-words: - Satellite, Multiple Access, ALOHA, Mobile Satellite Services, Average Packet Delay. 1 Introduction The main parameters in a multiple access techniques are the number of simultaneous users and the throughput of the network. Time Division Multiple Access (TDMA) and Code Division Multiple Access (CDMA) schemes offer high performances, but when the users do not generate information uniformly in the time, there is an important choice to obtain multiple access: Random Multiple Access (RMA) [1] [2] [3]. In this kind of multiple access the transmission media is employed simultaneously by the users, because they divide the information in packages. The users produce a non-uniform traffic, then the packages are transmitted in random times. This features are satisfied in rural applications, with VSAT terminals. The analyses of TDMA satellite systems is the deterioration of performance as the number of terminals increases irrespective of the total traffic in the system. The preamble bursts and guard times occupy a linear increase in the TDMA frame. The reason is the capacity is allocated to the sources, even when the source has nothing to send. Then, the RMA systems allocate bandwidth purely in response to traffic. The best performance in RMA when there are a large number of lightly loaded sources, see Figure 1. The paper has been organized in the following sections: section two is dedicated to ALOHA system, section three shows the analysis of pure ALOHA system, section four is dedicated to analyze the slotted ALOHA variation, section five is completely related to evaluate the performance of the average packet delay in this kind of system. Fig. 1 Satellite Multiple Access System. 2 ALOHA System The origin of the random multiple access technique was in the ALOHA system at the University of Hawaii. This system was a packet switched network, in which a radio channel was shared among a number of users. When a user generates a package, it is transmitted immediately regardless of the status at the other users in the system [4] [5] [6]. It is clear, that in this system is possible to collide packages, when two or more users generate simultaneously a package. The result of a collision ISBN: ISSN:

2 is two or more unintelligible packages and their retransmissions. In Figure 2 the line flow of pure ALOHA channel is illustrated. It is important to emphasize the collision presented in this Figure, when users one and two, transmit a package simultaneously. Afterward, the users involved in the collision should retransmit their packages after different random time-out intervals. The random variable of the timeout should have a large enough variance, then the probability of repeated collisions is small. Nevertheless, if the variance is too large, the delay of a package can increase drastically [6] [7]. P Collision = e 2Λm 1 (2) P Collision Probability of a collision. Λ Total average rate, packages/s. In order to carry the analysis forward it is assumed that the total traffic on the line has a Poisson distribution. In Figure 3, the pure ALOHA collision mechanism is illustrated. Fig. 2.Line flow on the pure ALOHA channel. There are many mechanisms to apprised of a collision, the easiest way is to detect the use of the channel and other way is to wait a positive acknowledgement when the packet is received correctly [9] [10] [11]. 3 Pure ALOHA Throughput The main assumptions in ALOHA systems are: the users generate fixed-length packages at a Poisson rate and, there are a lot of lightly loaded users, so that each holds no more than a single package at a time. The dimensionless offered load to communication channel can be obtained by equation 1 [11] [12] [13]. ρ = mλ (1) ρ Offered load. λ Average rate, packages/s. m Package o message duration, s. In order to be stable, in the absence of overhead traffic, the offered load must be less than one. The flow in the line consists of new packages and retransmitted packages. Then, the total rate should consider both. In this way, the probability of a collision can be calculated by equation 2. Fig. 3 Pure ALOHA collision mechanism. A package will be involved in a collision if another terminal transmits in a window with a duration equal to double package duration. The total average rate is the result of mixed traffic, see equation 3. 2Λm ( 1 ) Λ = λ + ΛP Collision = λ + Λ e (3) Then, the performance of pure ALOHA system can be calculated by equation 4. ( ) ρ = R exp 2R (4) R Total carried load on the channel, package/s. 4 Slotted ALOHA System The performance of the pure ALOHA system can be increased by changing the collision window, see Figure 4. The throughput in ALOHA system is determined by equation 5,[8] [9] [10]. ( ) ρ = R exp R (5) ISBN: ISSN:

3 Q r Probability of a successful retransmission after r retries. Then, the average retransmission delay of a packet is evaluated by equation 9. E{ T} = E{ r} 2 (9) Fig. 4 Slotted ALOHA Mechanism. 5 Average Packet Delay in ALOHA The ALOHA system gives a much better average packet delay in comparison with TDMA or CDMA systems [4] [5] [6]. It is important to point out that equation 4 is double-valued function, because for a given value for ρ, there are two values for R. This indicates that as the channel increases past 0.5, the throughput drops, because the number of collisions increases and there are more packet retransmissions. The condition explained before is named instability and it is an inherent feature in ALOHA, subsequently it is necessary to prevent it, by operating below the maximum throughput. The average packet delay in an ALOHA channel T ALOHA consists of the service time m (packet length or duration), the average retransmission delay D and the satellite propagation delay T R, see equation 6. T = T + m D (6) ALOHA R + Consider the randomized retransmission strategy in case of collision, where the random time delay introduced is uniformly distributed over 1 to K intervals of m seconds each. The retransmission delay after r retransmissions is computed by equation 7. T = r 2 (7) In these conditions, the average number of retransmissions of a packet is obtained by equation 8. { } r = r= E rq r (8) 1 The probability of a successful retransmission after r retries is a function determined by equation 10. q Q r r ( 1 q)( 1 q' ) 1 q' = (10) Probability of a successful transmission of a new packet. q Probability of a successful retransmission of a packet. For a large K, the average number of retransmissions can be approximated by equation 11. { r} = exp( 2R) 1 E (11) Thus the average retransmission delay of a packet is obtained by equation 12. D = E{ T} = [ exp( 2R) 1] 2 (12) Finally, putting all these results together we obtain the average packet delay approximation, see equation 13. ( K 1) m + TALOHA = TR + m + [ exp( 2R) 1] TR + 2 (13) It is very important to highlight that the equation 13 is double-valued function. 6 Results The performance of pure ALOHA is shown in Figure 5. ISBN: ISSN:

4 10, 50 and 100 (dark blue, blue and yellow, respectively). Fig. 5 Pure ALOHA throughput. In Figure 6, the performance of slotted ALOHA is illustrated. Fig. 6 Slotted ALOHA throughput. Fig. 7 Average Packet Delay in Slotted ALOHA system. The main result of this paper is shown in Figure 7, where the average packet delay is plotted for K = 7 Conclusions The main parameter of performance in RMA is the average packet delay, because it is the most important advantage of this multiple access technique in comparison with TDMA or CDMA. In this paper this parameter has been evaluated. The work presented here demonstrates that RMA is the best solution in packet networks, where the number of the sources is very high and the traffic is bursty and when the satellite channel capacity is limited. Now, the results of this article are being improved to obtain the performance of the slotted ALOHA system using a Markov chain embedded at the slot boundaries. References: [1] Timothy Pratt, Charles Bostian & Jeremy Allnutt, Satellite Communications, John Wiley & Sons, Second Edition, [2] International Telecommunication Union, Handbook on Satellite Communications, John Wiley & Sons, Third Edition, Suiza [3] Carleial A. B., Helman M. E., Bistable Behavior of ALOHA-type systems, IEEE Transactions on Communications, Vol. COM- 23, No. 4, April 1975, pp [4] Chu W. W., Konheim A. G., On the Analysis and Modeling of a class of Computer Communication Systems, IEEE Transactions on Communications, Vol. 20, No. 11, June 1972, pp [5] Kleinrock L., Lam S. S., Packet Switching in a Multiaccess Broadcast Channel: Performance Evaluation, IEEE Transactions on Communications, Vol. COM-23, No. 4, April 1975, pp [6] Lam S. S., Kleinrock L., Packet Switching in a Multiaccess Broadcast Channel: Dynamic Control Procedures, IEEE Transactions on Communications, Vol. COM-23, No. 9, September 1975, pp [7] Meditch J. S., Lee C. T., Stability and Optimization of the CSMA and CSMA/CD Channels, IEEE Transactions on Communications, Vol. COM-31, No. 6, June 1983, [8] Saadawi, T. N. Ephremedes A. Analysis, Stability and Optimization of slotted ALOHA with a finite number of buffered users, IEEE ISBN: ISSN:

5 Transactions on Automatic Control, Vol. AC- 26, No.3, June 1981, [9] Tobagi F. A., Carrier Sense Multiple Access with Message Based Priority Functions, IEEE Transactions on Communications, Vol. COM- 30, No. 1, January [10] Tsybakov B. S., Survey of USSR contributions to random multi-access communications, IEEE Transactions on Information Theory, Vol. 31, No. 2, March 1985, pp [11] Jacobs I. M., Binder R., Hoversten E. V. General Purpose Packet Satellite Networks, Proceedings of the IEEE, Vol. 66, No. 11, pp [12] Raychaudhuri D. Stability, Throughput and Delay of Asynchronous Selective Reject ALOHA, IEEE Transactions on Communications, Vol. COM-35, No. 7, 1987, pp [13] Retnadas G. Satellite Multiple Access Protocols, IEEE Communications Magazine, Vol. 18, No. 5, pp ISBN: ISSN: