Analysis of Manufacturing Systems

1. fntroduction We consider poliing systems where service is given in batches of unlimited size. When the server visits a queue, all customers present are served in a single batch. We call tlis gated batch seruice. The batch service time is independent of the size of the batch. Some examples of such systems are discussed in the literature below. Examples more related to manufacturing are ovens, transportation of material by one server to a number of different machines and, a,s an approximation, situations in which the set-up time is an order of magnitude larger than the actual production time. Literature reu'iew Polling systems with unlimited batch service have been studied much less extensively then those in which service is given to customers in a 'one at a time' fashion or in batches of limited size. Unlimited batch service models are considered in the context of teletext, videotex and TDMA systerrs, as well as for central data-base operations. Ammar and Wong [1987] studied a teletext system with l[ queues, fed by independent Poisson arrivai streams. Service times in all queues are deterministic (slotted, unit time each), there are no switch-over times, and the service discipline is locally gated. They showed that the policy which minimizes mean response time is of a cyclic natute, with cycle length L >N slots, in which" queue i is visited ki times, where |,l:rko: L. Yet, the problem of finding the exact length -L was only partially resolved. Liu and Nain [1992] examined a TDMA model with both the locally gated and exhaustive regimes for the case of. zero switching times and homogeneous arrival process to all queues. Dykeman et al. [1986j used Howard's poiicy-iteration algorithm to control a videotex system. They indicated that, even with equal and deterministic service requirements, and with no switching times, the structure of the optimal policy could be very complicated. Van Oyen and Teneketzis [1996] formulated a central data base system and an Automated Guided Vehicle as a polling system with an infinite.capacity batch service and zero switching times, where the controller observes only the length of the queue at which the server is located. Van der Wal and Yechiali [2003] explored dynamic server's visit-order policies in non-syrnmetric polling systems with switch-in and switch-out times, where service is in batches of unlimited size. They concentrated on so-called 'Hamiltonian tour' policies in which in order to give a fair treatment to the various queues the server attends every non-empty queue exactly once during each cycle. The server then dynamically generates a new visit schedule at the start of each