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The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues
Journal of the ACM, 1984Consider a closed cyclic queueing system consisting of M exponential queues. The Laplace-Stieltjes transform of the joint distribution of the consecutive sojourn times of a customer at the M queues is determined and shown to have a product form. The proof is based on a reversibility argument.
Boxma, O.J., Kelly, F.P., Konheim, A.G.
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Sojourn time distributions in tandem batch-networks
ACM SIGMETRICS Performance Evaluation Review, 2014The joint probability distribution of a customer's sojourn times in passing through a tandem pair of geometric batch-queues is obtained as a Laplace-Stieltjes transform (LST). The results obtained relate to a customer that passes, within a full batch, between the queues rather than being discarded in a partial batch.
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Sojourn time distribution in a stochastic compartmental system
Communications in Statistics - Theory and Methods, 1983Sojourn time distribution of an immigrant particle In a multi-compartmental system, total number of particles present in the system at any time and total time spent by all the particles in the system in any interval of time have been studies. Special cases are discussed.
P.R. Parthasarathy, P. Mayilswami
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Laplace transformation of the distribution of the time of system sojourns within a band
Automatic Control and Computer Sciences, 2009A stepped jump process of a semi-Markov walk with two delay screens at zero and at a is constructed. The Laplace transformation of the distribution of the time of the system sojourn within a given band and its first and second moments are found.
Tamilla I. Nasirova, R. I. Sadikova
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Queues with Equally Heavy Sojourn Time and Service Requirement Distributions
Annals of Operations Research, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Sojourn time distribution in polling systems with processor-sharing policy
Performance Evaluation, 2017Abstract We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service.
Bara Kim, Jeongsim Kim
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Distribution of sojourn time for a Brownian motion with jumps
Journal of Mathematical Sciences, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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THE SOJOURN TIME DISTRIBUTION OF AN ALTERNATING RENEWAL PROCESS
Australian Journal of Statistics, 1989summaryOrdinary, modified, and equilibrium alternating renewal processes are defined in such a way that the distribution of the sojourn time in one state of a two‐state system may be considered conditional on the starting state. The double Laplace transform of a non‐negative stochastic process is also defined, and used to express a result of Takacs ...
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A note on the distribution of sojourn time in a Markov chain
Trabajos de estadistica y de investigacion operativa, 1969A general formula for the distribution of sojourn time in a Markov chain bas been derived by Takacs [2]. Some special cases of that distribution are considered in this paper. The methods of deriving the distributions are elementary and quite different from that of Takacs.
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Sojourn time distributions in the queue defined by a general QBD process
Queueing Systems, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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