Strategic Equilibria in Queues with Dynamic Service Rate and Full Information

TL;DR

This paper analyzes customer equilibrium behavior in a queue with a dynamic service rate controlled by a threshold policy, considering full information and strategic customer decisions to maximize their net benefits.

Contribution

It introduces a model of customer behavior in a queue with a threshold-based dynamic service rate, providing equilibrium analysis under full information.

Findings

Characterizes equilibrium strategies based on queue length and service policy.

Shows how dynamic service control influences customer joining behavior.

Provides insights into optimal threshold settings for service rate control.

Abstract

We consider the problem of customer equilibrium behavior of a single server Markovian queue with dynamic control of the service rate. Customers arrive according a Poisson procedure and the system administrator makes a service rate choice between a low and a high value according to a $T$-threshold dynamic service policy, where the decision for switching to the higher service rate is made when the number of customers exceeds T without any additional cost. We assume that customers are identical and they are making join decisions regarding the maximization of their expected net benefit, receiving a fixed reward for service completion and incurring a waiting cost. In addition, we consider the observable case of the model where customers are fully informed on the service policy and the queue length upon arrival.