Gaussian skewness approximation for dynamic rate multi-server queues with abandonment. (English) Zbl 1285.60091
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 [N. Gans, G. Koole and 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 [Y. M. Ko and N. Gautam, INFORMS J. Computing; A.Mandelbaum et al., Queueing Syst. 30, No. 1–2, 149–201 (1998; Zbl 0911.90167); 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.
Reviewer: Vyacheslav Abramov (Melbourne)
MSC:
| 60K25 | Queueing theory (aspects of probability theory) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 90B22 | Queues and service in operations research |
Keywords:
multi-server queues; abandonment; dynamical systems; asymptotics; time-varying rates; time inhomogeneous Markov processes; Hermite polinomials; fluid and diffusion limits; skewness; cumulant momentsCitations:
Zbl 0911.90167References:
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