G-RAND: A phase-type approximation for the nonstationary G(t)/G(t)/s(t)+G(t) queue

We present a Markov model to analyze the queueing behavior of the nonstationary G(t)/G(t)/s(t)+G(t) queue. We assume an exhaustive service discipline (where servers complete their current service before leaving) and use acyclic phase-type distributions to approximate the general interarrival, service, and abandonment time distributions. The time-varying performance measures of interest are: (1) the expected number of customers in queue, (2) the variance of the number of customers in queue, (3) the expected number of abandonments, and (4) the virtual waiting time distribution of a customer arriving at an arbitrary moment in time. We refer to our model as G-RAND since it analyzes a general queue using the randomization method. A computational experiment shows that our model allows the accurate analysis of small- to medium-sized problem instances.