This NSF grant will provide funding for the development of algorithms and supporting theory for numerical analysis and approximation of general arrival/service-process queueing networks having time-dependent input parameters, characteristics and protocols. The result will be QNATS, the Queueing Network Approximator for Time-Dependent Systems---an addition to the NSF Cyberinfrastructure of web-useable software that is available to the engineering and scientific community. QNATS will include the facility to analyze systems in which arrival and service mechanisms change with time, as well as queueing nodal capacity and the number of servers. Also considered will be deterministic additions/deletions of entities from queueing nodes as a function of time. QNATS will allow for time-dependent interarrival- and service-time distributions that are general in shape, rather than the often unrealistic time-dependent exponential/Poisson distributions of textbook models. QNATS models will be easy to build and QNATS analysis will be able to deliver results quickly enough to be used interactively via web services
Queueing models are among the most widely used techniques to design and improve the performance of manufacturing, service-sector, digital-telecommunications and computer systems. In fact, queueing models are useful for assessing the performance of additions to the Cyberinfrastructure itself. Virtually any system in which discrete entities contend for resources from one or more service nodes can be represented as a network of queues. For example, time-dependent, infinite-server queueing networks have become a standard model for analysis of cellular telecommunication systems. Other applications come from a large variety of fields, including population processes in biology, migration/immigration processes, and epidemiology. QNATS will allow engineers and scientists in many fields to avoid the disastrous consequences that can occur when time-varying system characteristics are ignored or are approximated by their time-averaged values, leading to severe underestimation of system congestion.
