The Busy Period of an M/G/1 Queue with Customer Impatience

Onno Boxma, David Perry, Wolfgang Stadje, Shelley Zacks
2010 Journal of Applied Probability  
We consider an M/G/1 queue in which an arriving customer does not enter the system whenever its virtual waiting time, i.e. the amount of work seen upon arrival, is larger than a certain random patience time. We determine the busy period distribution for various choices of the patience time distribution. The main cases under consideration are exponential patience and a discrete patience distribution.
doi:10.1239/jap/1269610821 fatcat:fudp7se3ovh3hjheo36g62uroa