Abstract
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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