A Numerical Approach to Waiting Line Problems

Queuing problems formulated by equations (2.4) and (2.5) are, in general, very difficult to solve, particularly when the distributions of Xn+1 and Yn are arbitrary functions of the temporal parameter n. One of the few available time-dependent solutions treating model parameters as arbitrary functions of time considers no more than the simple M/M/1 queue (Clarke, [1953]). Approximations, or the use of simulation, sometimes provide tentative answers to those waiting line problems for which the difficulties in direct analysis are formidable. However, approximations may not always be satisfactory, while simulation inter alia suffers substantially from large computational requirements.