Waiting time and workload in queues with periodic Poisson input
- 1 March 1989
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 26 (02) , 390-397
- https://doi.org/10.1017/s0021900200027376
Abstract
This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].Keywords
This publication has 9 references indexed in Scilit:
- Approximation of periodic queuesAdvances in Applied Probability, 1987
- A Markov chain approach to periodic queuesJournal of Applied Probability, 1987
- Upper Bounds for Single Server Queues with Doubly Stochastic Poisson ArrivalsMathematics of Operations Research, 1986
- The asymptotic behavior o queues with time-varying arrival ratesJournal of Applied Probability, 1984
- 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
- Limit theorems for periodic queuesJournal of Applied Probability, 1977
- Investigation of waiting time problems by reduction to Markov processesActa Mathematica Hungarica, 1955