Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers

2017 ◽  
Vol 256 (1) ◽  
pp. 187-195 ◽  
Author(s):  
Hendrik Baumann ◽  
Werner Sandmann
Keyword(s):  
Markovian Arrival Process ◽  
Arrival Process ◽  
Tandem Queue ◽  
Finite Buffers ◽  
Phase Type ◽  
Service Times ◽  
Multi Server

A BMAP/PH/N SYSTEM WITH IMPATIENT REPEATED CALLS

2007 ◽  
Vol 24 (03) ◽  
pp. 293-312 ◽  
Author(s):  
VALENTINA I. KLIMENOK ◽  
DMITRY S. ORLOVSKY ◽  
ALEXANDER N. DUDIN
Keyword(s):  
Markov Chain ◽  
Time Distribution ◽  
Arrival Process ◽  
Service Time Distribution ◽  
State Distribution ◽  
Unsuccessful Attempt ◽  
Batch Markovian Arrival Process ◽  
Repeated Calls ◽  
Phase Type ◽  
Multi Server

A multi-server queueing model with a Batch Markovian Arrival Process, phase-type service time distribution and impatient repeated customers is analyzed. After any unsuccessful attempt, the repeated customer leaves the system with the fixed probability. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Stability condition and an algorithm for calculating the stationary state distribution of this Markov chain are obtained. Main performance measures of the system are calculated. Numerical results are presented.

The infinite server queue with semi-Markovian arrivals and negative exponential services

1972 ◽  
Vol 9 (1) ◽  
pp. 178-184 ◽  
Author(s):  
Marcel F. Neuts ◽  
Shun-Zer Chen
Keyword(s):  
Discrete Time ◽  
Infinite Number ◽  
Queue Length ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Infinite Server ◽  
Server Queue ◽  
Service Times ◽  
Negative Exponential ◽  
Stationary Probabilities

The queue with an infinite number of servers with a semi-Markovian arrival process and with negative exponential service times is studied. The queue length process and the type of the last customer to join the queue before time t are studied jointly, both in continuous and in discrete time. Limiting stationary probabilities are also obtained.

scholarly journals Analysis of retrial queue with heterogeneous servers and Markovian arrival process

Informatics ◽  
2020 ◽  
Vol 17 (1) ◽  
pp. 29-38
Author(s):  
Mei Liu
Keyword(s):  
Retrial Queue ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Service Rate ◽  
Heterogeneous Servers ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
System Effectiveness ◽  
Multi Server ◽  
Stationary Probabilities

Multi-server retrial queueing system with heterogeneous servers is analyzed. Requests arrive to the system according to the Markovian arrival process. Arriving primary requests and requests retrying from orbit occupy an available server with the highest service rate, if there is any available server. Otherwise, the requests move to the orbit having an infinite capacity. The total retrial rate infinitely increases when the number of requests in orbit increases. Service periods have exponential distribution. Behavior of the system is described by multi-dimensional continuous-time Markov chain which belongs to the class of asymptotically quasi-toeplitz Markov chains. This allows to derive simple and transparent ergodicity condition and compute the stationary probabilities distribution of chain states. Presented numerical results illustrate the dynamics of some system effectiveness indicators and the importance of considering of correlation in the requests arrival process.

The infinite server queue with semi-Markovian arrivals and negative exponential services

1972 ◽  
Vol 9 (01) ◽  
pp. 178-184 ◽  
Author(s):  
Marcel F. Neuts ◽  
Shun-Zer Chen
Keyword(s):  
Discrete Time ◽  
Infinite Number ◽  
Queue Length ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Infinite Server ◽  
Server Queue ◽  
Service Times ◽  
Negative Exponential ◽  
Stationary Probabilities

The queue with an infinite number of servers with a semi-Markovian arrival process and with negative exponential service times is studied. The queue length process and the type of the last customer to join the queue before time t are studied jointly, both in continuous and in discrete time. Limiting stationary probabilities are also obtained.

scholarly journals Analysis of an MMAP/PH1, PH2/N/∞ queueing system operating in a random environment

2014 ◽  
Vol 24 (3) ◽  
pp. 485-501 ◽  
Author(s):  
Chesoong Kim ◽  
Alexander Dudin ◽  
Sergey Dudin ◽  
Olga Dudina
Keyword(s):  
Random Environment ◽  
Queueing System ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Contact Center ◽  
Phase Type Distribution ◽  
Phase Type ◽  
Multi Server

Abstract A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented

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