SOME RESULTS FOR INFINITE SERVER POISSON QUEUES
Abstract
A generalization of the M/G/infinity queueing system with batch arrivals to one with time dependent arrival rates, service times, and batch size distributions is considered. It is shown that both W(t), the number of people being served at t, and S(t), the number of people who have completed service by t, are distributed as compound Poisson laws. The distributions of the traffic time average (the integral from 0 to T of the quantity W(t)dt)/T and the occupation time 0(t) (the amount of time past t until the system becomes empty, under the assumption that no new customers are served after t) are also derived. The limiting proportion of busy time and the asymptotic behavior of the traffic time average are also discussed in the time homogeneous case.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1968
- Accession Number
- AD0676893
Entities
People
- Mark O. Brown
- Sheldon M. Ross
Organizations
- University of California, Berkeley