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- Title
TIME-DEPENDENT SOLUTION OF A PRIORITY QUEUE WITH BULK ARRIVAL.
- Authors
Hawkes, A. G.
- Abstract
The time-dependent distribution of the number of customers in the queue and the lapsed service time is obtained, in terms of Laplace transforms, for a head-of-the-line priority queue in which both classes of customer arrive in bunches. From this we obtain the equilibrium distribution and the distribution of the number of customers left behind a departing customer. The latter is then used to find the equilibrium distribution of queuing times for both classes of customer. It is not easy to obtain a complete explicit solution, even for exponential service times, but the mean queuing times are readily obtained.
- Subjects
QUEUING theory; BULK queues; BUSINESS mathematics; CONSUMERS; MATHEMATICAL models; DISTRIBUTION (Probability theory); PROBABILITY measures
- Publication
Operations Research, 1965, Vol 13, Issue 4, p586
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.13.4.586