The Waiting Time Distribution of a TypekCustomer in a Discrete-Time MMAP[K]/PH[K]/c (c = 1, 2) Queue Using QBDs

DOI10.1081/STM-120028391zbMath1054.60098MaRDI QIDQ4451556

Benny Van Houdt, Chris Blondia

Publication date: 26 February 2004

Published in: Stochastic Models (Search for Journal in Brave)

zbMATH Keywords

waiting timeMarkovian arrival processQBDmultiple customer types

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (7)

Workload Process, Waiting Times, and Sojourn Times in a Discrete TimeMMAP[K/SM[K]/1/FCFS Queue] ⋮ Fitting correlated arrival and service times and related queueing performance ⋮ A batch arrival $M^X/M/c$ queue with impatient customers ⋮ Analysis of the adaptive \(MMAP[K/PH[K]/1\) queue: a multi-type queue with adaptive arrivals and general impatience] ⋮ Analysis of a continuous time SM[K/PH[K]/1/FCFS queue: age process, sojourn times, and queue lengths] ⋮ Response Time Distribution in a D-MAP/PH/1 Queue with General Customer Impatience ⋮ Age process, workload process, sojourn times, and waiting times in a discrete time SM[K/PH[K]/1/FCFS queue]

Cites Work

• Markov chains with marked transitions
• The delay distribution of a type k customer in a first-come-first-served MMAP[K/PH[K]/1 queue]
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• The workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority
• Queues with marked customers
• The versatility of MMAP[K and the MMAP[K]/G[K]/1 queue]
• Queue length distribution in a FIFO single-server queue with multiple arrival streams having different service time distributions

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