On priority queues with impatient customers

Abstract

In this paper, we study three different problems where one class of customers is given priority over the other class. In the first problem, a single server receives two classes of customers with general service time requirements and follows a preemptive-resume policy between them. Both classes are impatient and abandon the system if their wait time is longer than their exponentially distributed patience limits. In the second model, the low-priority class is assumed to be patient and the single server chooses the next customer to serve according to a non-preemptive priority policy in favor of the impatient customers. The third problem involves a multi-server system that can be used to analyze a call center offering a call-back option to its impatient customers. Here, customers requesting to be called back are considered to be the low-priority class. We obtain the steady-state performance measures of each class in the first two problems and those of the high-priority class in the third problem by exploiting the level crossing method. We furthermore adapt an algorithm from the literature to obtain the factorial moments of the low-priority queue length of the multi-server system exactly.

Dynamic control of a single-server system with abandonments

“…Related work includes that of Argon et al [2], who show that for a clearing system with abandonments, the policy that minimizes the number of abandonments is that which serves jobs with the shortest lifetime and shortest service time (assuming that they can be ordered this way). The performance of strict priority policies is studied in Iravani and Balcıoglu [14], but no optimality results are obtained. In [22,23] Ward and Glynn study single-class systems with abandonments.…”

Ant colony optimization for job shop scheduling using multi-attribute dispatching rules

“…Over the recent years in literature, there have been a lot of papers with respect to scheduling problems both for non-preemptive [3][4][5] and preemptive disciplines [6][7][8]. Dispatching rules are widely accepted in the industry because of the ease of implementation, satisfactory performance, low computational requirements, and the flexibility to incorporate domain knowledge and expertise [9].…”

On a doubly dynamically controlled supermarket model with impatient customers

“…Readers may refer to some important publications for more details, among which are the M/M/1 queue with impatient customers by Choi et al [16], Brandt and Brandt [14] and Altman and Yechiali [1]; the M/M/c queue with impatient customers by Stanford [44], Bhattacharya and Ephremides [5], Boxma and de Waal [7], Movaghar [40], Brandt and Brandt [13], Boots and Tijms [6], Yechiali [52] and Perel and Yechiali [43]; the GI/M/s queue with impatient customers by Teghem [47], Swensen [45] and Perry et al [42]; the M/G/ 1 queue with impatient customers by de Kok and Tijms [21], Bae et al [4], Perry and Asmussen [41], Martin and Artalejo [36], Boxma et al [8], Iravani and Balcıoğlu [25] and Boxma et al [9]; and the GI/G/1 queue with impatient customers by Daley [19], Baccelli and Hébuterne [3] and Baccelli et al [2]. The matrixanalytic method is applied to study queues with impatient customers, e.g., see Combé [18], Choi et al [17], Van Velthoven et al [49] and Chakravarthy [15].…”