Comparisons of multi-server queues with finite waiting rooms
- 1 January 1992
- journal article
- research article
- Published by Informa UK Limited in Communications in Statistics. Stochastic Models
- Vol. 8 (4), 719-732
- https://doi.org/10.1080/15326349208807248
Abstract
In this paper we consider s-server queues with capacity c, 1 ≤ s ≤ c ≤ ∞, the first-come first-served queue discipline and very general arrival and service processes. We show that the admission epochs and departure epochs decrease, so that the throughput increases, when any of the following changes occur: (1) the number of servers s increases, (2) the capacity c increases, (3) the external arrival counting process increases or (4) the service times decrease, provided that the service times are assigned in order of service initiation and that a subsequence ordering is used to compare arrival counting processes. The subsequence ordering for the arrival processes is very important for obtaining positive results with finite waiting rooms. The subsequence ordering holds between a superposition point process and its component point processes. The subsequence ordering can often be applied via its stochastic generalization, the stochastic subsequence ordering, which is implied by a failure rate ordering.Keywords
This publication has 5 references indexed in Scilit:
- Counterexamples for comparisons of queues with finite waiting roomsQueueing Systems, 1992
- Monotonicity and convexity properties of rate control throttlesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1990
- Comparing counting processes and queuesAdvances in Applied Probability, 1981
- Comparing multi-server queues with finite waiting rooms, II: Different numbers of serversAdvances in Applied Probability, 1979
- Comparing multi-server queues with finite waiting rooms, I: Same number of serversAdvances in Applied Probability, 1979