On parallel and series non homogeneous bulk arrival queueing model
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On parallel and series non homogeneous bulk arrival queueing model A. V. S. Suhasini & K. Srinivasa Rao & P. R. S. Reddy
Accepted: 19 January 2013 # Operational Research Society of India 2013
Abstract Queueing models create lot of importance due to their ready applicability. Much work has reported in literature regarding queueing models with homogeneous Poisson arrivals. But in many practical situations arising at places like transportation, communication networks, production processes, etc., the arrivals are non homogeneous and time dependent. Hence, in this paper we develop and analyze a queueing model with non homogeneous (time dependent) bulk arrivals under parallel and series configuration. Using the difference differential equations the joint probability density function of the number of customers in each queue is obtained. The performance of the model is evaluated by deriving the explicit expressions of the system characteristics like the probability of the system emptiness, average number of customers in each queue, the mean waiting time of the customer, the throughput of the nodes, etc. The sensitivity analysis of the model revealed that the bulk size distribution parameters and non homogeneous arrivals have significant influence on the system performance measures. The utility of the model in congestion control is demonstrated through a numerical illustration. Keywords Non homogeneous . Poisson process . Bulk arrivals . Parallel and series configuration . Tandem queueing model
1 Introduction A queue is a waiting line of unit demanding service at a service facility. Queueing models create lot of importance due to their ready applicability in several places like Data voice A. V. S. Suhasini (*) : P. R. S. Reddy Department of Statistics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India e-mail: [email protected] P. R. S. Reddy e-mail: [email protected] K. S. Rao Department of Statistics, Andhra University, Visakhapatnam, Andhra Pradesh, India e-mail: [email protected]
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transmission, Satellite and telecommunications, computer communications, transportation, production processes etc. Starting from the pioneering work by Erlang [10] remarkable progress has been made in queueing theory and its applications. In many of the realistic situations the output from one queueing process servers as a input to another. This sort of queueing systems are known as tandem or serial queues Srinivasa Rao et al. [24]. One of the potential string in developing queueing models is replacing some of the assumption where a more realistic nature can be employed. The major constituent processes of great importance in queueing systems are arrival and service processes. It is customary to consider that these two processes are independent of the queue size. But, this assumption is meaningful only when the queuing models are developed in a single environment. However, in some systems like communication networks, production processes, machine repairing etc., the service rate is dependent on the number of units
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