A pseudoconservation law for a time-limited service polling system with structured batch poisson arrivals

We consider a cyclic-service queueing system (polling system) with time-limited service, in which the length of a service period for each queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes empty, whichever occurs first, and then proceeds to the next queue. The customer whose service is interrupted due to the timer expiration is attended according to the nonpreemptive service discipline. For the cyclic-service system with structured batch Poisson arrivals (Mx/G/1) and an exponential timer, we derive a pseudoconservation law and an exact mean waiting time formula for the symmetric system.