On generalized hysteretic control queues with modulated input and state dependent service

Abstract

The authors study M/G/l type queues with modulated bulk input, state dependent batch service, and (r,N)-hysteretic discipline of idle and busy periods. In one of the models, the system has customers, that arrive during start-up periods, join the first servicing batch not in excess of server capacity..The analysis of the models is based on semi-regenerative and first excess level techniques developed by the first author and it yielded explicit formulas for the stationary distribution of the queuing process and other characteristics

Keywords:

• Queueing Process
• First Excess Level Process
• First Passage Time
• Termination Index
• Quorum
• N-policy
• Hysteresis
• Bulk Input
• Batch Service
• Fluctuation Theory
• Eembedded Markov Chain
• Equilibrium
• Semi-Regenerative Processes
• Modulated Process