Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods
In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distribution...
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| Veröffentlicht in: | Mathematics (Basel) 2021-12, Vol.9 (24), p.3236, Article 3236 |
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| creator | Vishnevsky, Vladimir Klimenok, Valentina Sokolov, Alexander Larionov, Andrey |
| description | In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples. |
| doi_str_mv | 10.3390/math9243236 |
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| subjects | Algorithms Computer networks Customer services Customers Finite capacity heterogeneous customers Internet of Things loss probabilities Machine learning marked Markovian arrival process Markov analysis Mathematics multi-server queueing system Performance evaluation Physical Sciences priorities Priority systems Probability Queuing theory Science & Technology Servers Traffic capacity |
| title | Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods |
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