Load balancing and routing games with admission price

We consider load balancing with routing games in a multiclass traffic environment. The servers are M/M/1 type servers and charge an admission price to each customer that joins the queue for service. Service requirements of all arriving customers are i.i.d. and they can receive service from any of the servers. Customers also have a waiting time cost that is proportional to their expected waiting times. Arrivals are from a multiclass population with the different classes differing in the their waiting time costs and having different arrival rates. In this paper we consider the following two load balancing schemes. (1) Both classes are non atomic; each arriving customer independently chooses one of the servers with a probability that optimizes an individual objective function. (2) One of the classes has a dispatcher that routes customers of that class to the servers with probabilities that minimize the total cost for that class; customers of the other class choose a server like in the first scheme. We analyze the equilibrium behavior of both the systems. We also describe a system that can be used to bound the price of anarchy in such systems.