A Heterogeneous Fork-Join Queueing System in Which EachJob Occupy All Free Servers

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Аннотация

In this paper, we consider a multiserver queueing system with heterogeneous servers in whicheach job is split to be serviced into a number of tasks, one for each free server. The tasks areserviced independently, but service time depends on weight of the tasks. A job is considered tobe complete only when all the tasks associated with the job have been executed to completion.Applying a matrix-geometric approach, we obtain the exact expression for the stationarydistribution of the number of jobs in the system under exponential assumptions. Using thedistribution, we derive other important performance measures. Special attention is paid to thesojourn time in the queueing system (the time to complete a job). Finally, some numericalexamples and a section of conclusions commenting the main research contributions of thispaper are presented.The results can be used for the performance analysis of multiprocessor systems and othermodern distributed systems.

Авторлар туралы

O Osipov

Saratov State University (SSU)

Хат алмасуға жауапты Автор.
Email: oleg.alex.osipov@gmail.com

Osipov O. A. - assistant of Department of System Analysis and Automatic Control of Saratov State University (SSU)

83 Astrahanskaya St., Saratov, 410012, Russian Federation

Әдебиет тізімі

  1. R. Corrˆea, I. Dutra, M. Fiallos, F. Gomes (Eds.), Models for Parallel and Distributed Computation, Springer US, 2002. doi: 10.1007/978-1-4757-3609-0.
  2. Y. Narahari, P. Sundarrajan, Performability Analysis of Fork-join Queueing Systems, Journal of the Operational Research Society 46 (10) (1995) 1237–1249. doi: 10.1057/jors.1995.171.
  3. L. Flatto, S. Hahn, Two Parallel Queues Created by Arrivals with Two Demands I, SIAM Journal on Applied Mathematics 44 (5) (1984) 1041–1053. doi: 10.1137/0144074.
  4. R. Nelson, A. N. Tantawi, Approximate Analysis of Fork/Join Synchronization in Parallel Queues, IEEE Transactions on Computers 37 (6) (1988) 739–743. doi: 10.1109/12.2213.
  5. S.-S. Ko, R. F. Serfozo, Response Times in

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