Queues with marked customers

He, Qi–Ming

doi:10.2307/1428072

Cited by 98 publications

(46 citation statements)

References 17 publications

(33 reference statements)

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“…For more information about the , MMAP its parameters and features, see (He, 1996). Characteristics of the MMAP influenced by the RE are given in (Dudin and Nazarov, 2015).…”

Section: Mathematical Modelmentioning

confidence: 99%

Queueing System Operating in Random Environment as a Model of a Cell Operation

Kim¹,

Dudin²,

Dudina³

et al. 2016

Industrial Engineering and Management Systems

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We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.

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“…For more information about the , MMAP its parameters and features, see (He, 1996). Characteristics of the MMAP influenced by the RE are given in (Dudin and Nazarov, 2015).…”

Section: Mathematical Modelmentioning

confidence: 99%

Queueing System Operating in Random Environment as a Model of a Cell Operation

Kim¹,

Dudin²,

Dudina³

et al. 2016

Industrial Engineering and Management Systems

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“…To extend the DBM AP process to distinguish more than one class or more than one priority of arrivals, we take a similar approach as the Markovian chain with marked transitions model in [7,8] and extend the one-dimensional index for the D k matrices in Section 2.1 to a two-dimensional index below. We consider an n state discrete-time Markovian arrival process with two types of batch arrivals, one for high priority jobs and the other for low priority jobs.…”

Section: The Dbmap Arrival Process With Prioritiesmentioning

confidence: 99%

“…Check the right-hand side of (8), the first factor (A k + R k+1 (0) A −1 ) is greater than A k , and the second factor (I −A 0 −R 1 (0) A −1 ) −1 is greater than I by referring to (7). Therefore, the product of the two factors is greater than R k (0) .…”

Section: Setmentioning

confidence: 99%

A matrix-analytic solution for the DBMAP/PH/1 priority queue

Zhao¹,

Li²,

Cao

et al. 2006

Queueing Syst

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Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBM AP ) has been widely used to model the source behavior of data traffic, while phase-type (P H) distribution has been extensively applied to model the service time. This paper focuses on the computation of the DBM AP/P H/1 queueing system with priorities, in which the arrival process is considered to be a DBM AP with two priority levels and the service time obeys a discrete P H distribution. Such a queueing model has potential in performance evaluation of computer networks such as video transmission over wireless networks and priority scheduling in ATM or TDMA networks. Based on matrix-analytic methods, we develop computation algorithms for obtaining the stationary distribution of the system numbers and further deriving the key performance indices of the DBM AP/P H/1 priority queue.

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“…Both a continues and a discrete time version of the MMAP[K] arrival process has been introduced [31,27], but we restrict ourselves to the discrete time variant. We shall distinguish between two types of MMAP [K] processes: those that allow for batch arrivals to occur, and those that do not.…”

Section: Markovian Arrival Process With Marked Arrivalsmentioning

confidence: 99%