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Stochastic control of K-parallel and series queuing model and its applications

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Abstract

Queuing models create lot of interest due to their ready applicability in the analysis of several congestion control systems. In this paper, we develop and analyze K-parallel and series queuing systems which is connected in a single network. Here, it is assumed that there are ‘K’ queues Q 1, Q 2, …, Q k which are connected in parallel and connected in series to another queue Q k+1 . Here the arrivals are in bulk and follows a compound Poisson process. It is assumed that the service completions in K nodes is load dependent and follow Poisson processes. Using the difference differential equations the joint probability generating function of number of customers in each queue is derived. The system performance measures such as average number of customers in each queue, the probability of the system emptiness, the average waiting time of a customer, throughput of the queues and the variability of system size distribution in each queue are derived and analyzed through numerical illustrations. The utility of this model in queue line control is demonstrated through applying it at Tirumala Tirupati Devasthanam which deals with pilgrims is also discussed. It is observed that the load dependent strategy reduces the congestion in queues and mean delays.

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Author information

Authors and Affiliations

  1. Department of Statistics, Sri Venkateswara University, Tirupati, AP, India

    P. Rajasekhara Reddy

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

    K. Srinivasa Rao

  3. Department of Statistics, Pondicherry University, Puducherry, India

    M. Venkateswaran

Authors
  1. P. Rajasekhara Reddy
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  2. K. Srinivasa Rao
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  3. M. Venkateswaran
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Correspondence to M. Venkateswaran.

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Rajasekhara Reddy, P., Srinivasa Rao, K. & Venkateswaran, M. Stochastic control of K-parallel and series queuing model and its applications. Int J Syst Assur Eng Manag 7 (Suppl 1), 178–197 (2016). https://doi.org/10.1007/s13198-015-0358-2

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  • DOI: https://doi.org/10.1007/s13198-015-0358-2

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