Nonstationary queues with interrupted Poisson arrivals and unreliable/repairable servers
A queueing model having a nonstationary Interrupted Poisson arrival process (IPP(t)), s time-dependent exponential unreliable/repairable servers and finite capacity c is introduced, and an approximation method for analysis of it is developed and tested. Approximations are developed for the time-dependent queue length moments and the system viewpoint waiting time distributions and moments. The approximation involves state- space partitioning and numerically integrating partial-moment differential equations (PMDEs). Surrogate distribution approximations (SDA's) are used to close the system of PMDEs. The approximations allow for analysis using only \((s+1)(s+6)\) differential equations for the queue length moments rather than the \(2(c+1)(s+1)\) equations required by the classic method of numerically integrating the full set of Kolmogorov-forward equations. Effectively hours of cpu time are reduced to minutes for even modest capacity systems. Approximations for waiting time distributions and moments are developed.
nonstationary Interrupted Poisson arrival process
scientific article; zbMATH DE number 4086710
scientific article