Approximation of periodic queues
- 1 March 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 19 (03) , 691-707
- https://doi.org/10.1017/s0001867800016827
Abstract
In this paper we demonstrate how some characteristics of queues with the periodic Poisson arrivals can be approximated by the respective characteristics in queues with Markov modulated input. These Markov modulated queues were recently studied by Regterschot and de Smit (1984). The approximation theorems are given in terms of the weak convergence of some characteristics and their uniform integrability. The approximations are applicable for the following characteristics: mean workload, mean workload at the time of day, mean delay, mean queue size.Keywords
This publication has 8 references indexed in Scilit:
- On ross's conjectures about queues with non-stationary poisson arrivalsJournal of Applied Probability, 1982
- On queues with periodic Poisson inputJournal of Applied Probability, 1981
- Queues with non-stationary input stream: Ross's conjectureAdvances in Applied Probability, 1981
- Some Useful Functions for Functional Limit TheoremsMathematics of Operations Research, 1980
- Stochastic Partial OrderingThe Annals of Probability, 1978
- Point processes and random measuresAdvances in Applied Probability, 1977
- Limit theorems for periodic queuesJournal of Applied Probability, 1977
- On the relation between customer and time averages in queuesJournal of Applied Probability, 1971