A fluid model for systems with random disruptions
Operations Research - Supplement to Operations Research: stochastic processes
A storage model with a two-state random environment
Operations Research - Supplement to Operations Research: stochastic processes
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
Invited Fluid queues with long-tailed activity period distributions
Computer Communications
Clearing Models for M/G/1 Queues
Queueing Systems: Theory and Applications
EXACT RESULTS FOR A FLUID MODEL WITH STATE-DEPENDENT FLOW RATES
Probability in the Engineering and Informational Sciences
PRODUCTION-INVENTORY MODELS WITH AN UNRELIABLE FACILITY OPERATING IN A TWO-STATE RANDOM ENVIRONMENT
Probability in the Engineering and Informational Sciences
A TANDEM FLUID QUEUE WITH GRADUAL INPUT
Probability in the Engineering and Informational Sciences
AN INTERMITTENT FLUID SYSTEM WITH EXPONENTIAL ON-TIMES AND SEMI-MARKOV INPUT RATES
Probability in the Engineering and Informational Sciences
Duality of dams via mountain processes
Operations Research Letters
A mountain process with state dependent input and output and a correlated dam
Operations Research Letters
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This paper is devoted to the analysis of a fluid queue with a buffer content that varies linearly during periods that are governed by a three-state semi-Markov process. Two cases are being distinguished: (i) two upward slopes and one downward slope, and (ii) one upward slope and two downward slopes. In both cases, at least one of the period distributions is allowed to be completely general. We obtain exact results for the buffer content distribution, the busy period distribution, and the distribution of the maximal buffer content during a busy period. The results are obtained by establishing relations between the fluid queues and ordinary queues with instantaneous input and by using level crossing theory.