Comparing multi-server queues with finite waiting rooms, I: Same number of servers

1 March 1979

journal article
research article
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 11 (02) , 439-447
https://doi.org/10.1017/s0001867800032614

Abstract

We compare two queueing systems with the same number of servers that differ by having stochastically ordered service times and/or interarrival times as well as different waiting room capacities. We establish comparisons for the sequences of actual-arrival and departure epochs, and demonstrate by counterexample that many stochastic comparisons possible with infinite waiting rooms no longer hold with finite waiting rooms.

Keywords

This publication has 10 references indexed in Scilit:

Comparing multi-server queues with finite waiting rooms, II: Different numbers of servers
Advances in Applied Probability, 1979
Stochastic Inequalities on Partially Ordered Spaces
The Annals of Probability, 1977
Bounds and Approximations in Queuing through Monotonicity and Continuity
Operations Research, 1977
Monotonicity and comparability of time-homogeneous markov processes with discrete state space
Mathematische Operationsforschung und Statistik, 1976
The Comparison Method for Stochastic Processes
The Annals of Probability, 1975
Stochastic bounds for heterogeneous-server queues with Erlang service times
Journal of Applied Probability, 1974
Stochastic Order Relationships Between GI/G/k Systems
The Annals of Mathematical Statistics, 1972
On the Optimality of Single-Server Queuing Systems
Operations Research, 1970
Ordered Families of Distributions
The Annals of Mathematical Statistics, 1955
On the theory of queues with many servers
Transactions of the American Mathematical Society, 1955