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We study the MAP/M/s+G queuing model with MAP (Markovian Arrival Process)arrivals, exponentially distributed service times, infinite waiting room, andgenerally distributed patience times. Using sample-path arguments, we proposeto obtain the steady-state distribution of the virtual waiting time andsubsequently the other relevant performance metrics of interest for theMAP/M/s+G queue by means of finding the steady-state solution of a properlyconstructed Continuous Feedback Fluid Queue (CFFQ). The proposed method isexact when the patience time is a discrete random variable and isasymptotically exact when it is continuous/hybrid for which case discretizationof the patience time distribution and subsequently the steady-state solution ofa Multi-Regime Markov Fluid Queue (MRMFQ) is required. Besides the steady-statedistribution, we also propose a new method to approximately obtain the firstpassage time distribution for the virtual and actual waiting times in the$MAP/M/s+G$ queue. Again, using sample-path arguments, finding the desireddistribution is also shown to reduce to obtaining the steady-state solution ofa larger dimensionality CFFQ where the deterministic time horizon is to beapproximated by Erlang or Concentrated Matrix Exponential (CME) distributions.Numerical results are presented to validate the effectiveness of the proposedmethod.

The MAP/M/s+G Call Center Model with General Patience Times: Stationary Solutions and First Passage Times