A tandem queue with a specialist server operating with a vacation strategy
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In the queueing system considered, service is provided at two stations, station 1 and station 2 operating in tandem. The station 1 is a multiserver station, where c identical exponential servers work in parallel. Station 2 is equipped with a single phase type server called specialist server. Customers arrive to the station 1 according to a Markovian Arrival Process. An arriving customer directly enters into service at station 1, if at least one of the server is idle, otherwise joins an infinite queue. After receiving service at station1, customers either proceed to station2 or can exit the system. There is a finite buffer between two stations. When the buffer is not filled, a customer coming out of the station1 joins the buffer with a probability p or leaves out system with the complimentary probability 1-p. If the buffer is full, then all the customers coming out of the station1 are lost forever. The server at the station 2 will be turned on only if number of customers in the buffer reaches a threshold value. Once the server is turned on, the service will be rendered until the buffer is emptied. Stability condition for this system is established and stationary distribution is obtained using Matrix Analytic Methods. Various Performance measures are also calculated. Our model is motivated by a hospital situation, where stations 1 represent the causality clinic and specialist server represents an expert, giving consultation at the request of a threshold number of patients.
- 2018 September 22 - 12:00
- 20 min
- Stochastic Modeling and Applied Research of TechnologY
- 1. Stochastic Modeling and Applications