Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes

This paper proposes a methodology for computing numerical bounds on cumulative-time (i.e., the time spent in a specified set of states before entering another specified set of states) distributions over discrete state Markov processes. The methodology uses randomization procedures to compute results for appropriately defined transient Markov processes; the transient distribution computed is equivalent to the requisite cumulative-time distribution. A queueing application of the methodology to delay times in queueing networks is outlined and its efficacy is appraised by comparing the results with a sojourn time for a problem with a known distribution.