Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogeneous servers
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Publication:3897815
DOI10.1007/BF01025867zbMath0451.60085MaRDI QIDQ3897815
Yukio Takahashi, Marcel F. Neuts
Publication date: 1981
Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)
waiting timemulti-server queuesheterogeneous serversasymptotic resultsqueue lengthphase type distributionscomputational probabilitymatrix-geometric solutions
Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)
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SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION ⋮ Reduced systems in Markov chains and their applications in queueing theory ⋮ Analysis of the stationary \(E_ k/C_ 2/s\) queueing system ⋮ Matrix-analytic methods in queueing theory ⋮ Extremal models for the \(G I \slash G I \slash K\) waiting-time tail-probability decay rate ⋮ Analysis and optimization of systems with heterogeneous servers and jump priorities ⋮ Light tail asymptotics in multidimensional reflecting processes for queueing networks ⋮ Modelling of a \(\mathrm{MAP/PH(1)}\), \(\mathrm{PH}(2)/2\) production inventory system with multiple servers and production vacations ⋮ Group maintenance policies for an \(R\)-out-of-\(N\) system with phase-type distribution ⋮ An \(M/M/2\) queueing system with heterogeneous servers including one with working vacation ⋮ Matrix-geometric solution of a multiserver queue with Markovian group arrivals and Coxian servers ⋮ GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES ⋮ The abscissa of convergence of the laplace-stieltjes transform of a ph-distribution ⋮ Transient analysis of a two-heterogeneous servers queue with impatient behavior ⋮ Heterogeneous two-server queueing system with reverse balking and reneging ⋮ Analysis of MAP/PH(1), PH(2)/2 queue with Bernoulli vacations ⋮ Iterative solution of the \(M^{[x}/C_ 2/S/N\) queues] ⋮ An \(M/M/2\) queueing system with heterogeneous servers and multiple vacations ⋮ Light-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type ⋮ Analysis of R-out-of-N repairable systems: the case of phase-type distributions ⋮ A unified approach for large queue asymptotics in a heterogeneous multiserver queue ⋮ Maximum Queue Length and Waiting Time Revisited: Multserver G/G/c Queue ⋮ Analysis of \(R\) out of \(N\) systems with several repairmen, exponential life times and phase type repair times: an algorithmic approach ⋮ On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals
Cites Work
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- The probabilistic significance of the rate matrix in matrix-geometric invariant vectors
- Asymptotic exponentiality of the tail of the waiting-time distribution in a Ph/Ph/C queue
- Stationary waiting-time distributions in the GI/PH/1 queue
- A NUMERICAL METHOD FOR THE STEADY-STATE PROBABILITIES OF A G1/G/C QUEUING SYSTEM IN A GENERAL CLASS
- Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector
- Renewal processes of phase type
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