On the optimality of FCFS for networks of multi-server queues

We consider multi-server queues in which arriving customers can be assigned to different servers. For three models the optimality of assigning customers to the server with smallest workload, FCFS, is shown. In the first two models isolated queues are studied, their difference being that in the first the cost functions are related to the workload, while in the second the departure processes are compared. The third model is concerned with networks of multi-server queues. 1991 Mathematics Subject Classification: 60K25, 90B22

[1]  D. Daley.  Certain optimality properties of the first-come first-served discipline for G/G/s queues , 1987 .

[2]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[3]  A. W. Kemp,et al.  Applied Probability and Queues , 1989 .

[4]  Ger Koole,et al.  On the Shortest Queue Policy for the Tandem Parallel Queue , 1992 .

[5]  R. Wolff.  AN UPPER BOUND FOR MULTI-CHANNEL QUEUES , 1977 .

[6]  Jean C. Walrand,et al.  An introduction to queueing networks , 1989, Prentice Hall International editions.

[7]  Ronald W. Wolff,et al.  Upper bounds on work in system for multichannel queues , 1987, Journal of Applied Probability.

[8]  J. Shanthikumar,et al.  Extremal properties of the FIFO discipline in queueing networks , 1992, Journal of Applied Probability.

[9]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[10]  Ger Koole,et al.  On the Assignment of Customers to Parallel Queues , 1992, Probability in the Engineering and Informational Sciences.

[11]  Serguei Foss,et al.  Approximation of multichannel queueing systems , 1980 .

[12]  S. Asmussen,et al.  Applied Probability and Queues , 1989 .

[13]  Donald F. Towsley,et al.  Effects of service disciplines inG/GI/s queueing systems , 1992, Ann. Oper. Res..

[14]  D. Stoyan.  A critical remark on a system approximation in queueing theory , 1976 .

[15]  Anurag Kumar,et al.  Optimal control of arrivals to queues with delayed queue length information , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.