Date of Award
Doctor of Philosophy (PhD)
Management Science/Information Systems
Professor Diwakar Gupta
Professor Robert F. Love
Professor Terry D. Todd
A polling system is a cyclic queueing model with multiple customer classes and a single server. Each customer class has its own queue (station). After the server switches to a station, it serves customers waiting at that station according to a specified service regime, e.g., exhaustive, gated or globally gated. It then moves to the next station, following a strict cyclic order. These models have several application areas including computer and communication networks and multi-item production systems. For example, a Local Area Network (LAN) can be modeled as a polling system by defining the central processing unit as the server and the data transmission requests from each terminal as customers. Similarly, a multi-item production system can be modeled as a polling system by considering the flexible machining cell as the server and each product type as a different customer class. In most systems that polling models are used to represent, the server requires time to switch and/or setup before it may start serving a different customer class. These processes (switching/setup) may take considerable amounts of time, and when that happens, it is undesirable to setup for a product type if there are no (or only a few) jobs of that type in the system. Therefore, a server scheduling policy that ignores system state information can easily lead to suboptimal performance.
Whereas most previous studies on polling models have assumed that the server behaves independently of the state of the system, we discuss two kinds of state-dependent server scheduling rules: i) the threshold setups model, and ii) the threshold start-up model. In the former model, the server does not setup (and does not serve any customers) at a station at which it finds less than a critical number of waiting customers, called the setup threshold. In the latter model, the server starts idling each time the system becomes empty, and it stays idle until arrivals to the system reach a critical number, called the start-up threshold. The server then resumes service from the station where it had stopped. Our analysis makes it possible to compare system performance under these state-dependent server scheduling rules and state-independent rules.
In this dissertation the following results are achieved. We develop an exact analysis for the one-threshold setup model with two stations, and an efficient approximation for the same model with any number of stations. For the general threshold setups model, we construct a numerical solution technique which is near-exact for calculating queue length distributions and station mean waiting times. The threshold start-up model is analyzed in detail, and mathematically exact expressions for man station waiting times are obtained for both exhaustive and globally gated service regimes. For each model, the extension to the gated service regime is also discussed.
Günalay, Yavuz, "State Dependent Server Scheduling Rules in Polling Systems" (1996). Open Access Dissertations and Theses. Paper 2314.