Analysis of M/G/ 1 queueing model with state dependent arrival and vacation

Journal of Industrial Engineering International

دوره 8، شماره 1، فروردین 2012   

نویسندگان

Charan Jeet Singh^{* 1}؛ Madhu Jain²؛ Binay Kumar³

¹Department of Mathematics Guru Nanak Dev University, Amritsar, Punjab, 143005, India

²Department of Mathematics, Indian Institute of Technology, Roorkee, Roorkee, Uttarakhand, 247667, India

³Department of Mathematics, M.L.U. DAV College, Phagwara, Punjab, 144402, India

چکیده

This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a fixed duration or may continue to be available in the system for next service. Using the probability argument, we construct the set of steady state equations by introducing the supplementary variable corresponding to elapsed service time. Then, we obtain the probability generating function of the units present in the system. Various performance indices, such as expected number of units in the queue and in the system, average waiting time, etc., are obtained explicitly. Some special cases are also deduced by setting the appropriate parameter values. The numerical illustrations are provided to carry out the sensitivity analysis in order to explore the effect of different parameters on the system performance measures.

کلیدواژه‌ها

State dependent؛ Queue؛ Arbitrary service time؛ Vacation؛ Supplementary variable؛ Average queue length