Queues in tandem with customer deadlines and retrials

Abstract

We study queues in tandem with customer deadlines and retrials. We first consider a 2-queue Markovian system with blocking at the second queue, analyze it, and derive its stability condition. We then study a non-Markovian setting and derive the stability condition for an approximating diffusion, showing its similarity to the former condition. In the Markovian setting, we use probability generating functions and matrix analytic techniques. In the diffusion setting, we consider expectations of the first hitting times of compact sets.

Staffing Tandem Queues with Impatient Customers Application in Financial Service Operations

“…Let n i be the number of servers at Station i, and µ i be the service rate of Station i's servers, for i = 1, 2. Similar to Reed and Yechiali (2013), we assume Station 1 has a waiting room of infinite size, and Station 2 has a waiting room with m < ∞ spots. Note that by letting m approach ∞, we can approximate a general two-station tandem queue with infinite waiting rooms in both stations.…”