The priority of inbound calls over outbound calls modeled as a discrete-time retrial/delay system

Abstract

A one-server discrete-time queueing model is studied with two arrival streams. Both arrival streams are in batches and we distinguish between a stream of low-priority customers, who are put in a queue which is served on a first-come-first-served basis, and a stream of (primary) high-priority customers, who are served uninterruptedly when the batch of high-priority customers finds the server idle upon arrival. High-priority customers are treated as retrial customers, but once in the orbit they lose their high-priority status. The Late Arrival Setup is chosen with Delayed Access. The high-priority retrial customers can be interpreted as inbound calls, and the low-priority customers as outbound calls in a call-center. The joint steady-state distribution of the queue length of the low-priority customers and the orbit size of secondary retrial customers is studied using probability generating functions. Several performance measures will be calculated, such as the mean queue length of the low-priority customers and the orbit size of the secondary retrial customers.