Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911623260667904 |
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| author | Takine, Tetsuya |
| author_facet | Takine, Tetsuya |
| contents | This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being active, the k-th (k = 1, 2, ..., K) arrival stream feeds at least one customer to the queue, where the number of arriving customers depends on the state of the underlying Markov chain. Service times of class $k$ customers are independent and identically distributed according to a general distribution. For these queues, we derive explicit formulae for the mean waiting times of customers in each class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23572 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods Takine, Tetsuya Probability 60K25, 60K37 This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being active, the k-th (k = 1, 2, ..., K) arrival stream feeds at least one customer to the queue, where the number of arriving customers depends on the state of the underlying Markov chain. Service times of class $k$ customers are independent and identically distributed according to a general distribution. For these queues, we derive explicit formulae for the mean waiting times of customers in each class. |
| title | Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods |
| topic | Probability 60K25, 60K37 |
| url | https://arxiv.org/abs/2604.23572 |