We consider a general polling model with @math stations. The stations are served exhaustively and in cyclic order. Once a station queue falls empty, the server does not immediately switch to the next station. Rather, it waits at the station for the possible arrival of new work ("wait-and-see") and, in the case of this happening, it restarts service in an exhaustive fashion. The total time the server waits idly is set to be a fixed, deterministic parameter for each station. Switchover times and service times are allowed to follow some general distribution, respectively. In some cases, which can be characterised, this strategy yields strictly lower average queueing delay than for the exhaustive strategy, which corresponds to setting the "wait-and-see credit" equal to zero for all stations. This extends results of Pek "oz (Probability in the Engineering and Informational Sciences 13 (1999)) and of (Annals of Operations Research 112 (2002)). Furthermore, we give a lower bound for the delay for all strategies that allow the server to wait at the stations even though no work is present.
References that refer to polling models where the server may be waiting at a station are apparently rare. The main references for us are Pek " o z @cite_4 and @cite_13 .
@cite_13 @cite_4
2099066336 2414390159
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. A recent interesting paper Cooper, Niu, and Srinivasan @2 #! shows how for some cyclic production systems reducing setup times can surprisingly increase work in process+ There the authors show how in these situations the introduction of forced idle time can be used to optimize system performance+ Here we show that introducing forced idle time at different points during the production cycle can further improve performance in these situations and also in situations where the suggestions from @2# yield no improvement+