Abstract
This paper deals with a discrete-time bulk-serviceGeo/Geo/1queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at timen. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results.
Highlights
There has been a rapid increase in the literature on discrete-time queueing system with working vacations
This paper focuses on a discrete-time batch-service infinite buffer Geo/Geo/1 queueing system with multiple working vacations in which arrivals occur according to a geometrical input
If there are some customers being served after the server finishes a working vacation, the service interrupted at the end of a vacation is lost and it is restarted with service rate μb at the beginning of the following service period, which means that the regular busy period starts
Summary
There has been a rapid increase in the literature on discrete-time queueing system with working vacations. Over the last several years the discrete-time single server queues in batch service without vacations have been studied in Gupta and Goswami [10], Chaudhry and Chang [11], Alfa and He [12], and Yi et al [13] This type of queueing systems raise interest once more by many scholars such as Banerjee et al [14, 15], Claeys et al [16, 17]. This paper focuses on a discrete-time batch-service infinite buffer Geo/Geo/1 queueing system with multiple working vacations in which arrivals occur according to a geometrical input. By using embedded Markov chain approach, we obtained the operation rules of the one-step transition probability matrix, the average length at random slots, and the average waiting time for an arriving customer This model has potential applications in computer networks where jobs are processed in batches.
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