Insensitivity in queueing systems
- 1 March 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 13 (04) , 846-859
- https://doi.org/10.1017/s0001867800036545
Abstract
It is well known that the stationary distribution of the number of busy servers in the Erlang blocking system (M/G/c/c) depends on the service-time distribution only through its mean. This insensitivity property is shared by several other queueing systems. In this paper, we give simple sufficient conditions for determining if this insensitivity property holds for general queueing systems and related stochastic models. The conditions involve determining whether the solution of the stationary Markovian flow equations also solves certain restricted flow equations. The proof that these conditions are sufficient is direct and elementary.Keywords
This publication has 13 references indexed in Scilit:
- Insensitivity of steady-state distributions of generalized semi-Markov processes by speedsAdvances in Applied Probability, 1978
- A Generalization of Erlang's Loss System to State Dependent Arrival and Service RatesMathematics of Operations Research, 1978
- Insensitivity of Steady-state Distributions of Generalized Semi-Markov Processes. Part IIThe Annals of Probability, 1978
- Insensitivity of Steady-State Distributions of Generalized Semi-Markov Processes. Part IThe Annals of Probability, 1977
- Networks of queues and the method of stagesAdvances in Applied Probability, 1976
- Networks of queuesAdvances in Applied Probability, 1976
- An extension of Erlang's formulas which distinguishes individual serversJournal of Applied Probability, 1972
- Markov population processesJournal of Applied Probability, 1969
- On Erlang's FormulaThe Annals of Mathematical Statistics, 1969
- Equilibrium distributions for an open migration processJournal of Applied Probability, 1968