Queue Length and Busy Period Analysis for the M/G/1 Queue with Negative Arrivals

Doo Ho Lee; Hyun Min Park; Dae-Eun Lim

doi:10.17485/ijst/2015/v8i34/124368

Queue Length and Busy Period Analysis for the M/G/1 Queue with Negative Arrivals

Doo Ho Lee ¹, Hyun Min Park ², Dae-Eun Lim ³

Affiliations
1 Software Research Lab, ETRI, Daejeon, 305-700, Korea, Republic of
2 Department of Business Administration, Pai Chai University, Korea, Republic of
3 Department of System and Management Engineering, Kangwon National University, Korea, Republic of

Abstract
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In this paper, the queue lengths and the busy period lengths of the M/G/1 queueing systems with negative arrivals are analyzed. Two types of negative arrivals are considered. One type is negative customers and the other type is disasters. When a negative customer arrives to a system, one positive customer is removed if the number of positive customers is more than one. In particular, we assume the RCH (Removal of a Customer at the Head) type of negative customers which represent a kind of work-canceling signal to the positive customer in service. On the other hand, disasters get rid of all customers in the system. In this paper, the Probability Generating Function (PGF) of the stationary queue length and busy period length of M/G/1 queue with both negative customers and disasters are derived.