Transient analysis of the Erlang A model

Abstract

We consider the Erlang A model, or queue, with Poisson arrivals, exponential service times, and m parallel servers, and the property that waiting customers abandon the queue after an exponential time. The queue length process is in this case a birth–death process, for which we obtain explicit expressions for the Laplace transforms of the time-dependent distribution and the first passage time. These two transient characteristics were generally presumed to be intractable. Solving for the Laplace transforms involves using Green’s functions and contour integrals related to hypergeometric functions. Our results are specialized to the queue, the M / M / m queue, and the M / M / m / m loss model. We also obtain some corresponding results for diffusion approximations to these models.

Simulation of a Queuing System of a Post Office in Anylogic Software

“…An event represents a change in the state of the system at a time. There are two event types in simpler event-based simulation models arrival of customer and an end of service [10][11][12][13]. employee works with an information system.…”

“…Therefore it is advisable to use a simulation method to get the system model closer to the real system, as much as possible. Contribution of the simulation method is in the ability of capturing the dynamic side of the system and complicated probabilistic relationships [10][11][12][13][14][15].…”

New perspectives on the Erlang-A queue

“…Thus, it comes as no surprise that the Erlang-A model, which is a Markovian and multiserver queueing model that incorporates customer abandonments, is an important modeling tool in a multitude of application settings. Some of the more prominent applications include telecommunications and call/contact centers, healthcare, urban mobility and transportation, and more recently cloud computing; see, for example, [28], [29], [45], [37], [3], [5], [13], [48], [44], [2], [41], [20], [42], [12], and [4]. A detailed overview of the model can be found in [26].…”

Transient provisioning and performance evaluation for cloud computing platforms: A capacity value approach

“…Moving away from equilibrium analysis of these systems in favor of transient analysis allows provisioning to be performed over short time intervals in a way that is dependent on the current state of the system and knowledge of the arrival rate over the near future. Since obtaining analytic results for the transient distribution of loss network type systems is notoriously difficult, one often resorts to numerical inversion of Laplace transforms [3,24] or approximations [27]. In [13], its companion [12], and more recently [5] and [30], a useful alternative to the consideration of the transient distribution for queueing type models is proposed.…”