Abstract
In this paper, we study the behavior of the transmitter buffer of a system working under a Stop-and-Wait retransmission protocol. The buffer at the transmitter side is modeled as a discrete-time infinite-capacity queue. The numbers of information packets entering the buffer during consecutive slots are assumed to be independent and identically distributed random variables. The packets are sent over an unreliable channel and transmission errors occur in a correlated manner. Specifically, the probability of an erroneous transmission is modulated by a two-state Markov chain. An expression is derived for the probability generating function of the buffer content. This expression is then used to derive several queue-length characteristics and the mean packet delay. Numerical examples illustrate the strong effect of error correlation on the system performance. The obtained analytical results are also compared with appropriate simulations.
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References
Bhunia CT (2001) ARQ—review and modifications. IETE Tech Rev 18(5): 381–401
Bruneel H (1993) Performance of discrete-time queueing systems. Comput Oper Res 20(3): 303–320
Bruneel H, Steyaert B, Desmet E, Petit G (1994) Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues. Eur J Oper Res 76(3): 563–572
De Munnynck M, Lootens A, Wittevrongel S, Bruneel H (2002) Transmitter buffer behaviour of stop-and-wait ARQ schemes with repeated transmissions. IEE Proc Commun 149(1): 13–17
Fantacci R (1992) Performance evaluation of some efficient stop-and-wait techniques. IEEE Trans Commun 40(11): 1665–1669
Gail HR, Hantler SL, Taylor BA (1996) Spectral analysis of M/G/1 and G/M/1 type Markov chains. Adv Appl Probab 28(1): 114–165
Gantmacher FR (1959) The Theory of Matrices, Volume One. AMS Chelsea Publishing, Providence
Kim JG, Krunz M (1999) Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel. In: Proceedings of 2nd ACM international workshop on wireless mobile multimedia, WoWMoM, Seattle, USA, pp 59–66
Liinaharja M, Chakraborty SS (2002) Analysis and optimisation of an adaptive selective repeat scheme for time-varying channels with feedback errors. AEÜ (Int J Electron Commun) 56(3): 177–186
Moeneclaey M, Bruneel H, Bruyland I, Chung DY (1986) Throughput optimization for a generalized Stop-and-Wait ARQ scheme. IEEE Trans Commun 34(2): 205–207
Towsley D (1981) A statistical analysis of ARQ protocols operating in a nonindependent error environment. IEEE Trans Commun 27(7): 971–981
Towsley D, Wolf JK (1979) On the statistical analysis of queue lengths and waiting times for statistical multiplexers with ARQ retransmission schemes. IEEE Trans Commun 27(4): 693–702
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De Vuyst, S., Tworus, K., Wittevrongel, S. et al. Analysis of Stop-and-Wait ARQ for a wireless channel. 4OR-Q J Oper Res 7, 61–78 (2009). https://doi.org/10.1007/s10288-008-0072-x
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DOI: https://doi.org/10.1007/s10288-008-0072-x