Decomposition of the M/M/1 transition function

DOI10.1007/BF01158470zbMath0731.60086MaRDI QIDQ808110

Masaaki Kijima, Joseph Abate, Ward Whitt

Publication date: 1991

Published in: Queueing Systems (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviourqueue length processabsorbing barriertransient behaviourdependence of the relaxation time on the parameter of the initial geometric distribution

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Transition functions, generators and resolvents (60J35)

Related Items (4)

SCALING PROPERTIES OF QUEUES WITH TIME-VARYING LOAD PROCESSES: EXTENSIONS AND APPLICATIONS ⋮ \(\mathrm{M}/\mathrm{M}/1\) queue in two alternating environments and its heavy traffic approximation ⋮ A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation ⋮ On the number of customers lost in a finite state-dependent queue.

Cites Work

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• Transient behavior of the M/M/1 queue: Starting at the origin
• Simple spectral representations for the M/M/1 queue
• The correlation functions of rbm and m/m/1
• Transient behavior of the M/M/1 queue via Laplace transforms
• A sample path analysis of the M/M/1 queue
• A CHARACTERIZATION OF BIRTH AND DEATH PROCESSES

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