Price-rate tradeoff in a service system with two servers

The main goal of our study is to find the optimal service rate and service price to retain customers in a 2-servers service system where customers may flow to the quicker server. In common queuing systems, the initial demand is divided into equal demands to each server. But, when customers are wait too long in a queue, they may turn to join another queue which have an impact on effective arriving rate of each queue. We study this kind of phenomenon from a queueing game theoretic point of view. We start with studying the equilibrium performances in a general M/M/2 service system where customers join a single queue. Then we extent the results to the target service system and obtain the optimal service rate and service price of the system. Some sensitivity analysis are also included in this paper.