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We consider a polling system with two queues, exhaustive service, noswitch-over times and exponential service times. The waiting cost depends onthe position of the queue relative to the server: It costs a customer c pertime unit to wait in the busy queue (where the server is) and d per time unitin the idle queue (where no server is). Customers arrive according to a Poissonprocess. We study the control problem of how arrivals should be routed to thetwo queues in order to minimize expected waiting costs and characterizeindividually and socially optimal routing policies under three scenarios ofavailable information at decision epochs: no, partial and complete information.In the complete information case, we develop a new iterative algorithm todetermine individually optimal policies, and show that such policies can bedescribed by a switching curve. We conjecture that a linear switching curve issocially optimal, and prove that this policy is indeed optimal for the fluidversion of the two-queue polling system.

Optimal routing in two-queue polling systems