Abstract
We consider a M/G/1 queue modified such that an arriving customer may be totally or partially rejected depending on a r.v. (the barricade) describing his impatience and on the state of the system. Three main variants of this scheme are studied. The steady-state distribution is expressed in terms of Volterra equations and the relation to storage processes, dams and queues with state-dependent Poisson arrival rate is discussed. For exponential service times, we further find the busy period Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associated birth-death process.
Original language | English |
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Pages (from-to) | 105-130 |
Number of pages | 26 |
Journal | Queueing Systems |
Volume | 19 |
Issue number | 1-2 |
DOIs | |
State | Published - Mar 1995 |
Keywords
- Birth-death process
- Volterra equation
- busy period
- coupling
- impatient customers
- martingale stopping theorem
- queue
- storage process
- virtual waiting time
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics