Gaussian skewness approximation for dynamic rate multi-server queues with abandonment
The paper under review studies \(M(t)/M/c(t)+M\) queueing systems, where \(M(t)\) in the first position denotes a non-homogeneous Poisson arrival Process, \(M\) in the second position denotes exponentially distributed service time, \(c(t)\) denotes the number of agents (servers) at time \(t\) and \(+M\) in the last position denotes the exponential distribution for an abandonment time. This model is referred to as Erlang-A model, see [\textit{N. Gans}, \textit{G. Koole} and \textit{A. Mandelbaum}, ``Telephone call centers: tutorial, review and research prospects'', Manuf. Serv. Oper. Manag. 5, No. 2, 79--141 (2003)] and describes large scale service systems such as call centers or hospitals. The paper presents a simple method generating new algorithms that are successively better approximations of the stochastic dynamics for the \(M(t)/M/c(t)+M\) queueing system that are known for this type of system from the available literature, see [\textit{Y. M. Ko} and \textit{N. Gautam}, INFORMS J. Computing; \textit{A.Mandelbaum} et al., Queueing Syst. 30, No. 1--2, 149--201 (1998; Zbl 0911.90167); \textit{A. Mandelbaum} et al., ``Queue lengths and waiting times for multi-server queues with abandonment and retrials'', Telecommun. Syst. 21, 149--172 (2002)]. This is achieved by computing a low dimensional, deterministic dynamic system.
scientific article; zbMATH DE number 6236691
scientific article