On Queue-Length Information in a Tandem Queueing System

Abstract

We consider a system where customers have to go through two service phases. For example, patients who arrive to an ER first wait for being admitted and then wait to be seeing by a physician. Assuming patients are served according to the order of their arrival (FCFS), we study the case where queue-length information is available at arrival: customers observe the state of the entire system and decide whether to join or not. We calculate the equilibrium strategy and show that customer strategy is not necessarily a function of the total number of customers in the system. We also show that when customers join the system they might balk in front of the second queue, but never renege from the first queue. To learn the value of information we compare the observable system with a system in which queue-length information is only partially available: instead of observing the full system state, customers observe queue length only at arrival to each queue.