The busy period of the migi1 vacation model with a bernoulli schedule

Ravi Ramaswamy · L. D. Servi

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

The server busy period for the M|G|1 vacation model with a Bernoulli schedule is studied. Simple expressions are found for (i) the conditional joint distribution of the busy period and number in the system at the end of a busy period given the number in the system at the beginning of the busy period, (ii) the ergodic distribution of the number in the system at a busy period initiation epoch, and (iii) the distribution of the depletion time at service initiation epochs. Expressions in the real domain for the key ingredients of die busy period are also given.

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References

1986Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules 1985A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times 1986Average Delay Approximation of M/G/1 Cyclic Service Queues with Bernoulli Schedules 1983Mean-delay approximation for cyclic-service queueing systems 1989Blocking Probability for M/G/1 Vacation Systems with Occupancy Level Dependent Schedules 1987Dynamics of the M/G/1 Vacation Model

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1995Optimization of polling systems with Bernoulli schedules 2010On the discrete-time Geo/G/1 queue with randomized vacations and at most J vacations 2016Strategic joining rules in a single server Markovian queue with Bernoulli vacation 2013Performance analysis of an M/G/1 queueing system under Bernoulli vacation schedules with server setup and close down periods 1998Queues with hysteretic control by vacation and post-vacation periods 2005A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy 1997Analysis of a two-queue model with Bernoulli schedules

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