Time-dependent behavior of fluid buffer models with Markov input and constant output rates
SIAM Journal on Applied Mathematics
The busy period in the fluid queue
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Fluid models for single buffer systems
Frontiers in queueing
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Clearing Models for M/G/1 Queues
Queueing Systems: Theory and Applications
The M/G/1 Queue with Finite Workload Capacity
Queueing Systems: Theory and Applications
First Passage Times in Fluid Models with an Application to Two Priority Fluid Systems
IPDS '96 Proceedings of the 2nd International Computer Performance and Dependability Symposium (IPDS '96)
Queues with Workload-Dependent Arrival and Service Rates
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Mean first passage times in fluid queues
Operations Research Letters
Continuous feedback fluid queues
Operations Research Letters
Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility
Operations Research Letters
Duality of dams via mountain processes
Operations Research Letters
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We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical examples.