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September 2013 A duality approach to queues with service restrictions and storage systems with state-dependent rates
D. Perry, W. Stadje, S. Zacks
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J. Appl. Probab. 50(3): 612-631 (September 2013). DOI: 10.1239/jap/1378401226


Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain `dual' M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workload and the numbers of customers present in the systems as well as the distributions of the lengths of busy and idle periods. Moreover, we use the duality approach to study finite capacity storage systems with general state-dependent outflow rates. Here our duality leads to a Markovian finite storage system with state-dependent jump sizes whose content level process can be analyzed using level crossing techniques. We also derive a connection between the steady-state densities of the non-Markovian continuous-time content level process of the G/M/1 finite storage system with state-dependent outflow rule and the corresponding embedded sequence of peak points (local maxima).


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D. Perry. W. Stadje. S. Zacks. "A duality approach to queues with service restrictions and storage systems with state-dependent rates." J. Appl. Probab. 50 (3) 612 - 631, September 2013.


Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1282.60092
MathSciNet: MR3102505
Digital Object Identifier: 10.1239/jap/1378401226

Primary: 60K25
Secondary: 90B22

Keywords: Duality , G/M/1 , level crossing , M/G/1 , peak point , Queue with service restrictions , state-dependent rate , steady state , storage system

Rights: Copyright © 2013 Applied Probability Trust


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Vol.50 • No. 3 • September 2013
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