Probability in the Engineering and Informational Sciences



NEGATIVE PROBABILITIES AT WORK IN THE M/D/1 QUEUE


Henk  Tijms  a1 and Koen  Staats  a2
a1 Department of Econometrics and Operations Research, Vrije University, 1081 HV Amsterdam, The Netherlands, and, Tinbergen Institute Amsterdam, 1018 WB Amsterdam, The Netherlands, E-mail: tijms@feweb.vu.nl
a2 Department of Econometrics and Operations Research, Vrije University, 1081 HV Amsterdam, The Netherlands

Article author query
tijms h   [Google Scholar] 
staats k   [Google Scholar] 
 

Abstract

This article derives amazingly accurate approximations to the state probabilities and waiting-time probabilities in the M/D/1 queue using a two-phase process with negative probabilities to approximate the deterministic service time. The approximations are in the form of explicit expressions involving geometric and exponential terms. The approximations extend to the finite-capacity M/D/1/N + 1 queue.