Finite-Buffer Queues with Workload-Dependent Service and Arrival Rates |
| |
Authors: | René Bekker |
| |
Institution: | (1) Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands;(2) Philips Electronics, CWI, P.O. Box 94079, 1090, GB, Amsterdam, The Netherlands |
| |
Abstract: | We consider M/G/1 queues with workload-dependent arrival rate, service speed, and restricted accessibility. The admittance of customers typically depends on the amount of work found upon arrival in addition to its own service requirement. Typical examples are the finite dam, systems with customer impatience and queues regulated by the complete rejection discipline. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet.First, we compare the steady-state distribution of the workload in two finite-buffer models, in which the ratio of arrival and service speed is equal. Second, we find an explicit expression for the cycle maximum in an M/G/1 queue with workload-dependent arrival and service rate. And third, we derive a formal solution for the steady-state workload density in case of restricted accessibility. The proportionality relation between some finite and infinite-buffer queues is extended. Level crossings and Volterra integral equations play a key role in our approach.AMS subject classification: 60K25, 90B22 |
| |
Keywords: | restricted accessibility finite buffer impatience state-dependent rates workload cycle maximum level crossings Volterra integral equation |
本文献已被 SpringerLink 等数据库收录! |
|