Collaboration versus Specialization in Service Systems with Impatient Customers

TL;DR

This paper analyzes optimal server assignment policies in tandem queueing systems with impatient customers, demonstrating when servers should work together or separately to maximize throughput under various conditions.

Contribution

It provides a complete characterization of optimal policies in Markovian systems with task-dependent server efficiencies and customer impatience, including cases with server synergy.

Findings

Optimal policy often involves servers working together or at specific stations based on system state.

Throughput maximization depends on server skill levels, customer abandonment rates, and task-dependent synergy.

Numerical results illustrate how policies change with system parameters.

Abstract

We study tandem queueing systems in which servers work more efficiently in teams than on their own and customers are impatient in that they may leave the system while waiting for service. Our goal is to determine the server assignment policy that maximizes the long-run average throughput. We show that when each server is equally skilled at all tasks, the optimal policy has all the servers working together at all times. We also provide a complete characterization of the optimal policy for Markovian systems with two stations and two servers when each server's efficiency may be task dependent. We show that the throughput is maximized under the policy which assigns one server to each station (based on their relative skill at that station) unless station 2 has no work (in which case both servers work at station 1) or the number of customers in the buffer reaches a threshold whose value we characterize (in which case both servers work at station 2). We study how the optimal policy varies with the level of server synergy (including no synergy) and also compare the optimal policy for systems with different customer abandonment rates (including no abandonments). Finally, we investigate the case where the synergy among collaborating servers can be task-dependent and provide numerical results.