Approximations for the M/GI/N+GI type call center

Abstract

In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N + GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single server M/GI/1 + GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution is numerically computing the workload density function in the M/GI/1 + GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions. Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1 + GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.

A Markov Model for Measuring Service Levels in Nonstationary G(t)/G(t)/s(t)+G(t) Queues

“…Though stationary approximations are straightforward and generally applicable, additional challenges may arise in complex systems, for which the stationary model itself is intractable. For instance, the applicability of MOL to the M(t)/G/s(t) + G model necessarily relies on the availability and accuracy of approximations for the corresponding stationary M/G/s + G model (see Whitt [27] and Iravani and Balcioglu [28]). We refer to Green et al [7], Whitt [8] and Defraeye and Van Nieuwenhuyse [9] for further references on the stationary approximations available in the literature.…”

Tandem Queues with Impatient Customers for Blood Screening Procedures

“…Stanford [31] contains a brief literature review, and [22] provides a useful approximation for the waiting time distribution in M/G/N +G and several additional references on multiserver queues with impatience.…”

“…The latter system has been studied in [10], which paper allows the service time distribution to be general and depending on the batch size. As a final remark, we'd like to refer to [22] for approximations for performance measures of the M/G/N + G queue. It may be worthwhile to adapt their approach to the case of batch service.…”

The Busy Period of an M/G/1 Queue with Customer Impatience

“…Stanford [11] relates the waiting time distribution of the (successful) customers and the workload seen by an arbitrary arrival in G/G/1 + G. See Stanford [12] for a brief literature review, and [5] for an approximation for the waiting time distribution in M/G/N + G and several additional references on multiserver queues with impatience.…”