In this paper, single server queue with poisson arrivals, triple stages of service with service interruption & compulsory server vacation is considered. After the completion of first stage and second stage of service, the server must provide the third-stage of service. After the completion of each third stage of service, the server will take compulsory vacation. The vacation time is, exponentially distributed.The time dependent probability generating functions have been obtained in terms of Laplace transforms.
In this paper, we study about a M/G/1 Queuing model with single stage of service. Service interrupts during the time of service. The server does not get into the repair process immediately. It gets into a Set up time stage for the prior work to be done. On completion of set up stage service, the server will get into the repair process consisting of two stages, in which first stage is compulsory and the second stage of service is optional. For the model defined, we get the steady state results in closed form in terms of the probability generating functions and all the other execution performance measures of the model defined.
In this paper, a batch arrival non-Markovian queueing model with three types of service is considered.The customers arrive in batches of variable size.Here a single server provides three types of service ,type 1 with probability , type 2 with probability and type 3 with probability. The service times follows general distribution. The customer may choose either type of the services.The server follows multiple vacation.Whenever the system becomes empty, the server takes a vacation and the vacation follows general distribution.On returning from vacation if the server finds no customer waiting in the system,again the server goes for vacation.The system may breakdown at random and repair time follow exponential distribution. we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times.The probability generating function and some probability measures of the system are also found.
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