Queueing and risk models with dependencies

This paper analyzes various stochastic recursions that arise in queueing and insurance risk models with a ‘semi-linear’ dependence structure. For example, an interarrival time depends on the workload, or the capital, immediately after the previous arrival; or the service time of a customer depends o...

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Bibliographic Details
Published in:Queueing systems 2022-10, Vol.102 (1-2), p.69-86
Main Authors: Boxma, O. J., Mandjes, M. R. H.
Format: Article
Language:English
Subjects:
Business and Management
Computer Communication Networks
Control
Customer services
Laplace transforms
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Queueing
Random variables
Supply Chain Management
Systems Theory
Workloads
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Summary:This paper analyzes various stochastic recursions that arise in queueing and insurance risk models with a ‘semi-linear’ dependence structure. For example, an interarrival time depends on the workload, or the capital, immediately after the previous arrival; or the service time of a customer depends on her waiting time. In each case, we derive and solve a fixed-point equation for the Laplace–Stieltjes transform of a key performance measure of the model, like waiting time or ruin time.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-022-09863-7