A Two Server Poisson Queue With State Dependent Hybrid Service Discipline With Variant Breakdown

• Published in: Communications in Mathematics and Applications Vol. 15; no. 1; pp. 111 - 132
• Main Authors: Kalyanaraman, R., Anurathi, B.
• Format: Journal Article
• Language: English
• Published: Kingsville RGN Publications 01.01.2024
• Subjects: Breakdown; Cost analysis; Customer services; Customers; Poisson distribution; Probability distribution functions; Queuing theory; Random variables
• ISSN: 0976-5905; 0975-8607
• DOI: 10.26713/cma.v15i1.2531

A Poisson queue with two servers and with system breakdown has been considered in this paper. In addition, the servers are in homogeneous mode upto serving of N customers. After which the servers changed to heterogeneous mode. If the system is busy failure may occur to the system. As in the case of service policy, in a similar way two different breakdown policies are assumed. At the instant of breakdown, if there are N or less than N customers in the system the system is completely shutdown. Otherwise, the servers provides service with different service rates. The number of arrivals and the number of service completions follows different Poisson distributions. The interbreakdown periods follows negative exponential distributions. Immediately the repair process takes place. The repair periods are random variables, follows negative exponential distribution. This model is defined and the time independent solutions are derived. Also some system performance measures are obtained. To show the practical applicability of the model some numerical illustrations are provided. The corresponding cost model is defined and analyzed.