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Parallel and series queueing model with state and time dependent service

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Abstract

This paper deals with the development and analysis of a parallel and series tandem queueing model with state and time dependent service. The non-stationarity in service processes is characterised through non-homogeneous Poisson Process. In this model, the customers that after getting service at either of the first two service stations which are parallel, the customer joins the third queue, which is connected in tandem to “first two service stations”. This type of queueing systems are known as parallel and series queueing systems. The joint probability generating function of the queue size distribution of three queues is derived. The system performance measures such as average number of customers in each queue, the average waiting time of a customer in each queue, the throughput of the service station, utility of service station, the variance of the content of queue are derived. The sensitivity analysis with numerical illustration revealed that the time and state dependent service rates have significant influence on the system performance measures. This model is very helpful for controlling and monitoring the communication systems such as LAN, WAN and MAN.

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Acknowledgements

The authors are very much thankful to the referees and editor for their suggestion and valuable comments on the paper which has improved the quality of the paper.

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Authors and Affiliations

  1. SLDC, APTransco, Vidyut Soudha, Vijayawada, India

    J. Durga Aparajitha

  2. Department of Statistics, Andhra University, Visakhapatnam, India

    K. Srinivasa Rao

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  1. J. Durga Aparajitha
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  2. K. Srinivasa Rao
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Correspondence to J. Durga Aparajitha.

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Aparajitha, J.D., Srinivasa Rao, K. Parallel and series queueing model with state and time dependent service. OPSEARCH 60, 1626–1658 (2023). https://doi.org/10.1007/s12597-023-00667-8

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