Time Sensitive Functionals in a Queue with Sequential Maintenance

Abstract

We use semi-regenerative, fluctuations methods, and sequential games to examine a queueing system with server performing a secondary maintenance work. When the buffer becomes empty, the server leaves the system to service packets of jobs at a maintenance facility where his time there is restricted by T (a random time). He returns to the system when his sojourn time expires and if the last packet is fully processed. If the buffer contents is below N , the server departs from the system again to continue with maintenance; this time rendering just one packet at a time until the buffer is replenished. We obtain compact and explicit functionals for the queueing process in equilibrium for both discrete and continuous time parameter processes.

Current Trends in Random Walks on Random Lattices

“…It was introduced in Dshalalow [37] and further refined in [67] and then picked up in a series of papers. We just mention some: Agarwal, Dshalalow, and O'Regan [68], Al-Matar and Dshalalow [69], Dshalalow [70,71], Dshalalow and Bacot [72], Dshalalow and Nandyose [73,74], Dshalalow, Nandyose, and White [75], Dshalalow and White [76]. See further discussions in Sections 5 and 6.…”

“…This approach introduces some insurmountable uncertainty dependent on the crudeness of the observation process {τ n } ∞ n=1 . A sequence of papers, Dshalalow and his collaborators [50,68,69,[73][74][75][76]113] pursue methods referred to as time sensitive analysis that try to offer more precise look into the intermediate time period between the pre-exit observation and post-exit observation times during which the real time exit actually occurs, to glean some further insights about the process upon its exit.…”

Time sensitive analysis of independent and stationary increment processes

“…The time-sensitive tools can be utilized in other time-insensitive models, in particular in stochastic games, queueing, and finance [5,6]. In some earlier forms, time-sensitive analysis was known in queueing [2] (under the name of semi-regenerative techniques) and in other stochastic processes such as Cox [1] to interpolate stationary probabilities of embedded processes.…”

On the Exiting Patterns of Multivariate Renewal-Reward Processes with an Application to Stochastic Networks

“…Inverse D transforms will be evaluated in exact form using properties derived by Dshalalow and summarized in Appendix B of [45]. Many of the results have been used to invert the D operator in works from Dshalalow and his collaborators [36,46,47].…”