Analysis of a queueing system with a general service scheduling function, with applications to telecommunication network traffic control. (English) Zbl 1107.90009

Summary: We analyze a queueing system with a general service scheduling function. There are two types of customer with different service requirements. The service order for customers of each type is determined by the service scheduling function \(\alpha _{k}(i, j)\) where \(\alpha _{k}(i, j)\) is the probability for type-\(k\) customer to be selected when there are \(i\) type-1 and j type-2 customers. This model is motivated by traffic control to support traffic streams with different traffic characteristics in telecommunication networks (in particular, ATM networks). By using the embedded Markov chain and supplementary variable methods, we obtain the queue-length distribution as well as the loss probability and the mean waiting time for each type of customer. We also apply our model to traffic control to support diverse traffics in telecommunication networks. Finally, the performance measures of the existing diverse scheduling policies are compared. We expect to help the system designers select appropriate scheduling policy for their systems.


90B22 Queues and service in operations research
90B18 Communication networks in operations research
Full Text: DOI


[1] Choi, B. D.; Kim, Y. C.; Choi, D. I.; Sung, D. K., An analysis of M,MMPP/G/1 queues with QLT scheduling policy and Bernoulli schedule, IEICE Transactions on Communications, E81-B, 1, 13-22 (1998)
[2] Choi, D. I.; Choi, B. D.; Sung, D. K., Performance analysis of priority leaky bucket scheme with queue-length-threshold scheduling policy, IEE Proceedings of Communications, 145, 6, 395-401 (1998)
[3] Katayama, T.; Takahashi, Y., Analysis of a two-class priority queue with Bernoulli schedules, Journal of the Operations Research Society of Japan, 35, 3, 236-249 (1992) · Zbl 0771.60079
[4] Knessl, C.; Choi, D. I.; Tier, C., A dynamic priority queue model for simultaneous service of two traffic types, SIAM Journal on Applied Mathematics, 63, 2, 398-422 (2002) · Zbl 1034.60082
[5] Lee, D. S.; Sengupta, B., Queueing analysis of a threshold based priority scheme for ATM networks, IEEE/ACM Transactions on Networking, 1, 6, 709-717 (1993)
[6] Servi, L. D., Average delay approximation of M/G/1 cyclic service queues with Bernoulli schedules, IEEE Journal on Selected Areas in Communications, SAC-6, 6, 813-822 (1986)
[7] Sugahara, A.; Takine, T.; Takahashi, Y.; Hasegawa, T., Analysis of a nonpreemptive priority queue with SPP arrivals of high class, Performance Evaluation, 21, 215-238 (1995) · Zbl 0875.68084
[8] Takagi, H., Queueing Analysis, (Vacation and Priority Systems, vol. 1 (1991), North-Holland: North-Holland Amsterdam) · Zbl 0744.60114
[9] Yin, N.; Li, S. Q.; Stern, T. E., Congestion control for packet voice by selective packet discarding, IEEE Transactions on Communications, 38, 5, 674-683 (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.