Single-Server with Delay-Dependent Arrival Streams
- 1 April 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 2 (2) , 231-247
- https://doi.org/10.1017/s0269964800000759
Abstract
This paper derives the steady-state distribution of the virtual wait in GI/M1 queues in which the interarrival times depend on the virtual wait. Applications are queues in which the time it will take for the system to start servicing a new arrival (virtual wait) affects the generation of new arrivals. Such queues arise in airport or large-city freeway traffic control systems. Related state-dependent situations occur in production-inventory systems, cash flow in banking or in insurance systems, dam control systems, and in natural sciences. The method of analysis is by means of system-point level crossing theory.Keywords
This publication has 4 references indexed in Scilit:
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- The System Point Method in Exponential Queues: A Level Crossing ApproachMathematics of Operations Research, 1981
- An embedded level crossing technique for dams and queuesJournal of Applied Probability, 1979
- Single-Server Queues with Service Time Dependent on Waiting TimeOperations Research, 1973