Article

Queueing Systems

, Volume 68, Issue 3, pp 353-360

Conditional inter-departure times from the M/G/s queue

  • Casper VeegerAffiliated withDepartment of Mechanical Engineering, Eindhoven University of Technology
  • , Yoav KernerAffiliated withDepartment of Industrial Engineering and Management, Ben Gurion University of the Negev Email author 
  • , Pascal EtmanAffiliated withDepartment of Mechanical Engineering, Eindhoven University of Technology
  • , Ivo AdanAffiliated withDepartment of Mechanical Engineering, Eindhoven University of TechnologyDepartment of Quantitative Economics, University of Amsterdam

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Abstract

We study the mean and the distribution of the time elapsing between two consecutive departures from the stationary M/G/s queue given the number of customers left behind by the first departure is equal to n. It is conjectured that if the failure rate of the service time distribution is increasing (decreasing), then (i) the limit of the mean conditional inter-departure time as n tends to infinity is less (greater) than the mean service time divided by the number of servers s, and (ii) the conditional inter-departure times are stochastically decreasing (increasing) in n for all ns.

Keywords

Departure process Failure rate

Mathematics Subject Classification (2000)

60K25