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Infinite-server queues with Hawkes input
| Content Provider | Scilit |
|---|---|
| Author | Koops, D. T. Saxena, M. Boxma, O. J. Mandjes, M. |
| Copyright Year | 2018 |
| Description | In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a Markovian nature. We obtain a system of differential equations that characterizes the joint distribution of the arrival intensity and the number of customers. Moreover, we provide a recursive procedure that explicitly identifies (transient and stationary) moments. Subsequently, we allow for non-Markovian Hawkes arrival processes and nonexponential service times. By viewing the Hawkes process as a branching process, we find that the probability generating function of the number of customers in the system can be expressed in terms of the solution of a fixed-point equation. We also include various asymptotic results: we derive the tail of the distribution of the number of customers for the case that the intensity jumps of the Hawkes process are heavy tailed, and we consider a heavy-traffic regime. We conclude by discussing how our results can be used computationally and by verifying the numerical results via simulations. |
| Related Links | http://arxiv.org/pdf/1707.02196 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/29A985198A710AB1F7636DCEAEA9C0E6/S002190021800058Xa.pdf/div-class-title-infinite-server-queues-with-hawkes-input-div.pdf |
| Ending Page | 943 |
| Page Count | 24 |
| Starting Page | 920 |
| ISSN | 00219002 |
| e-ISSN | 14756072 |
| DOI | 10.1017/jpr.2018.58 |
| Journal | Journal of Applied Probability |
| Issue Number | 3 |
| Volume Number | 55 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-06-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of Applied Probability exciting Process Hawkes Process server Queue Branching Process tailed Distribution Heavy Traffic Primary 60k25 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistics, Probability and Uncertainty |
