Ergodicity conditions for queueing systems with repeated calls
Systems with repeated calls are closely related - as far as the analysis of the limiting behavior as the time {tau}{yields}{infinity} is concerned - to systems with restrictions [1, 2]. These systems are of interest to mathematicians mainly because their obvious importance in various applications (communication theory, air traffic control, information systems) when a customer who was refused service (an aircraft which cannot land in an airport because the landing strip is occupied) is directed into a standby position from which the demand for service is then repeated at random periods of time (an aircraft circles and then attempts another landing). A special feature of these systems is that even when there are customers at standby, the server may be idle, thus reducing the capacity of the system. Moreover, there can be restrictions on the duration of a customer at a standby position or on the number of repetitions allowed. Service disciplines may also vary. All this resulted in a wide variety of models with repeated calls especially in the engineering literature. Moreover, conditions for the existence of a stationary state are either not considered at all or are determined for special models under the simplest assumptions on the controlling sequence which allows us to utilize the known ergodicity criteria for Markov chains.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 412012
- Journal Information:
- Journal of Mathematical Sciences, Vol. 72, Issue 1; Other Information: PBD: 25 Oct 1994; TN: Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei; 3-8(1991)
- Country of Publication:
- United States
- Language:
- English
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