We consider polling models in the sense of Takagi (MIT Press, 1986). In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue instead of switching to the next station. We propose four different wait-and-see strategies that govern these waiting periods. We assume Poisson arrivals for new messages and allow general service and switchover time distributions. The results are formulas for the mean average queueing delay and characterisations of the cases where the wait-and-see strategies yield a lower delay compared to the exhaustive strategy.
@cite_16 , focus on a two-queue polling model with a timer as in Strategy IV at station @math which may be random. They examine different configurations: Either both stations are served exhaustively, or one station is controlled by the @math -limited protocol whereas the other station is served in an exhaustive fashion. The main results are the probability generating function of the queue lengths, expressions for pseudo-conservation laws, and the Laplace transform of the stationary waiting times.
@cite_16
2099066336
We consider two-queue polling models with the special feature that a timer mechanism is employed at Q1: whenever the server polls Q1 and finds it empty, it activates a timer and remains dormant, waiting for the first arrival. If such an arrival occurs before the timer expires, a busy period starts in accordance with Q1's service discipline. However, if the timer is shorter than the interarrival time to Q1, the server does not wait any more and switches back to Q2. We consider three configurations: (i) Q1 is controlled by the 1-limited protocol while Q2 is served exhaustively, (ii) Q1 employs the exhaustive regime while Q2 follows the 1-limited procedure, and (iii) both queues are served exhaustively. In all cases, we assume Poisson arrivals and allow general service and switchover time distributions. Our main results include the queue length distributions at polling instants, the waiting time distributions and the distribution of the total workload in the system.