Transient Analysis of K-node Tandem Forked Queuing Model with Bulk Arrivals Having Load Dependent Service Rates
M. Sita Rama Murthy1, K.Srinivasa Rao2, V. Ravindranath3, P.Srinivasa Rao4

1M.Sita Rama Murthy, Department of Basic Science, Vishnu Institute of Technology, Bhimavaram  (Andhra Pradesh), India.
2K.Srinivasa Rao, Department of Statistics, Andhra University, Visakhapatnam (Andhra Pradesh), India.
3V.Ravindranath, Department of Mathematics, Jawaharlal Nehru Technological University Kakinada, Kakinada (Andhra Pradesh), India.
4P.Srinivasa Rao, Department of Computer Science and Systems Engineering, Andhra University, Visakhapatnam (Andhra Pradesh), India.
Manuscript received on 01 May 2019 | Revised Manuscript received on 15 May 2019 | Manuscript published on 30 May 2019 | PP: 2124-2149 | Volume-8 Issue-7, May 2019 | Retrieval Number: G6135058719/19©BEIESP
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Abstract: In this paper a K-node series and parallel queuing model with load dependent service rates is introduced and analysed. It is assumed that the customers arrive to the initial queue in batches and wait for service. After completing the service at first service station they may join any one of the (K-1) parallel queues which are connected to first queue in series and exit from the system after getting service. Here it is assumed that the arrival and service completions follow Poisson processes and service rates depend on number of customers in the queue connected to it. Using difference-differential equations the joint probability function of number of customers in each queue is derived. The system performance measures such as average number of customers, waiting time of customer, variation of number of customers in each queue, throughput of each service station, utilization of each server are derived explicitly. The sensitivity of the model is analysed through numerical illustration and observed that the performance measures are significantly influenced by state dependent service rates. This model also includes the earlier models as particular cases for specific values of the parameters. This model is useful in analysing the practical situations such as communication networks, production process and cargo handling.
Keyword: Bulk Arrivals, Forked Queuing Model, Load Dependent Service rates, Performance of System, Poisson Process, Tandem Queue.
Scope of the Article: SOA and Service-Oriented Systems.