Abstract
The buffer contents in a discrete-time single-server queue is analyzed under a round-robin service discipline. This service discipline is related to the continuous-time processor-sharing discipline and models the operation of certain types of input-buffered ATM-switches when variable-length packets are routed. The packet-length distribution is arbitrary here but of phase-type. Through a generating-functions approach, a set of functional equations is derived from which a straightforward algorithm to calculate the mean buffer contents is obtained. Numerical examples illustrate the main characteristics of the round-robin service discipline and its relation to the first-come-first-serve service discipline. Hereby, implications for the performance of the input-buffered ATM-switches are given special attention.
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Asmussen, O., Nerman, O. and Olsson, M. (1996) Fitting phase-type distributions via the EM algorithm. Scandinavian Journal of Statistics, 23, 419–441.
Awdeh, R. and Mouftah, M. (1995) Survey of ATM switch architectures. Computer Networks and ISDN Systems, 27, 1567–1613.
Bruneel, H. and Kim, B. (1993) Discrete-time models for communication systems including ATM. Kluwer Academic Publishers, Boston.
Cao, X.-R. (1995) The maximum throughput of a nonblocking space-division packet switch with correlated destinations. IEEE Transactions on Communications, 43, 1898–1901.
Cao, X.-R. and Towsley, D. (1995) A performance model for ATM switches with general packet length distributions. IEEE/A CM Transactions on Networking, 3, 299–309.
Daduna, H. and Schassberger, R. (1981) A discrete-time round-robin queue with Bernoulli input and general arithmetic service time distributions. Acta Informatica, 15, 251–263.
Disney, R.L., Konig, D. and Schmidt, V. (1984) Stationary queue-length and waiting time distributions in single server feedback queues. Advances in Applied Probability, 16, 437–446.
Jacob, L. and Kumar, A. (1995) Saturation throughput analysis of an input queueing ATM switch with multiclass bursty traffic. IEEE Transactions on Communications, 43, 757–761
Jaiswal, N.K. (1982) Performance evaluation studies for time-sharing computer systems. Performance Evaluation, 2, 223–236.
Karol, M.J., Hluchyj, M.G. and Morgan, S.P. (1987) Input versus output queueing on a space-division packet switch. IEEE Transactions on Communications, 35, 1347–1356.
Kleinrock, L. (1976) Queueing systems, volume II: computer applications. Wiley, New York.
Laevens, K. and Bruneel, H. (1996a) Discrete-time queueing models with feedback for input-buffered ATM switches. Performance Evaluation, 2728, 71–87.
Laevens, K. and Bruneel, H. (1996b) Useful relations in the analysis of ATM-queues fed by multiple types of traffic. Electronics Letters, 32, 631–632.
Lam, S.S. and Shankar, A.U. (1981) A derivation of response time distributions for a multi-class feedback queueing system. Performance Evaluation, 1, 48–61.
Li, S.-Q. (1992) Performance of a nonblocking space-division packet switch with correlated input traffic. IEEE Transactions on Communications, 40, 97–108.
Muntz, R. (1972) Waiting time distributions for round-robin queueing systems. Proceedings Symposium on Computer and Communications Networks and Teletraffic (Brooklyn, 1972)
Neuts, M.F. (1981) Matrix-geometric solutions in stochastic models. John Hopkins University Press, Baltimore.
Petersen, J. (1991) Throughput limitation by head-of-line blocking. Proceedings ITC-13 (Copenhagen, 1991), 659–663.
Schassberger, R. (1981) On the response time in a discrete round-robin queue. Acta Informatica, 16, 57–62.
Schassberger, R. (1984) A new approach to the M/G/1 processor-sharing queue. Advances in Applied Probability, 16, 202–213.
Takâcs, L. (1963) A single-server queue with feedback. The Bell System Technical Journal, 42, 505–519.
van den Berg, J.L., Boxma, U.J. and Groenendijk, W.P. (1989) Sojourn times in the M/G/1 queue with deterministic feedback. Stochastic Models, 5, 115–129.
van den Berg, J.L. and Boxma, O.J. (1991) The M/G/1 queue with processor sharing and its relation to a feedback queue. Queueing Systems, 9, 365–40.
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© 1998 Springer Science+Business Media Dordrecht
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Laevens, K. (1998). The Round-Robin Service Discipline in Discrete Time for Phase-Type Distributed Packet-Lengths. In: Hasegawa, T., Takagi, H., Takahashi, Y. (eds) Performance and Management of Complex Communication Networks. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35360-9_19
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DOI: https://doi.org/10.1007/978-0-387-35360-9_19
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