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**A duality approach to queues with service restrictions and storage systems with state-dependent rates.**
*(English)*
Zbl 1282.60092

The authors develop the duality techniques for M/G/1 and G/M/1 type queueing processes. Specifically, they study two different queueing models, for which the duality techniques are developed. These are the queueing model 1 (specifically defined in the paper) with truncated service policy and the queueing model 2 (specifically defined in the paper) with the bounded waiting time policy. The first type model suggests that any service requirement that would increase the total workload beyond some constant capacity threshold is reduced such that this threshold can be reached but not exceeded. The second type model suggests that new arrivals whose waiting time in the queue would exceed some fixed constant are not admitted to the system. For these systems the authors derive the steady state distributions of the workload and the numbers of customers present in the systems as well as distributions of the length of busy and idle periods. The duality approach is used to study finite capacity storage systems with general state-dependent outflow rates. A connection is also derived 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 sequences of local maximum points.

Reviewer: Vyacheslav Abramov (Melbourne)

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

90B22 | Queues and service in operations research |

### Keywords:

queue with service restrictions; storage system; state-dependent rate; M/G/1 queues; \(G/M/1\) queues; steady state; duality; level-crossings; peak point
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\textit{D. Perry} et al., J. Appl. Probab. 50, No. 3, 612--631 (2013; Zbl 1282.60092)

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