A Multi-server Queueing Model with Markovian Arrivals and Phase Type Cooperative Services - Simulation Approach

2015 ◽  
pp. 1-12
Author(s):  
Srinivas R. Chakravarthy
Keyword(s):  
Queueing Model ◽  
Simulation Approach ◽  
Phase Type ◽  
Multi Server

ANALYSIS OF A MULTI-SERVER QUEUE WITH MARKOVIAN ARRIVALS AND SYNCHRONOUS PHASE TYPE VACATIONS

2009 ◽  
Vol 26 (01) ◽  
pp. 85-113 ◽  
Author(s):  
SRINIVAS R. CHAKRAVARTHY
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing System ◽  
Queueing Model ◽  
Waiting Time Distribution ◽  
Steady State Analysis ◽  
Phase Type ◽  
Server Queue ◽  
Qbd Process ◽  
Multi Server

We study a MAP/M/c queueing system in which a group of servers take a simultaneous phase type vacation. The queueing model is studied as a QBD process. The steady-state analysis of the model including the waiting time distribution is presented. Interesting numerical results are discussed.

scholarly journals Zero Queueing for Multi-Server Jobs

2021 ◽  
Vol 5 (1) ◽  
pp. 1-25
Author(s):  
Weina Wang ◽  
Qiaomin Xie ◽  
Mor Harchol-Balter
Keyword(s):  
Cloud Computing ◽  
Stability Region ◽  
Transient Analysis ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Hard Problem ◽  
Queueing Model ◽  
Multiple Servers ◽  
First Results ◽  
Multi Server

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

A Matrix-Analytic Solution to Three-Level Multi-Server Queueing Model with a Shared Finite Buffer

2022 ◽  
pp. 690-699
Author(s):  
Qigen Zhao ◽  
Chia-Hung Wang ◽  
Zhenyu Dong ◽  
Shumeng Chen ◽  
Qipeng Yang ◽  
...  
Keyword(s):  
Analytic Solution ◽  
Finite Buffer ◽  
Queueing Model ◽  
Multi Server

A MULTI-SERVER QUEUEING MODEL WITH MARKOVIAN ARRIVALS AND MULTIPLE THRESHOLDS

2007 ◽  
Vol 24 (02) ◽  
pp. 223-243 ◽  
Author(s):  
SRINIVAS R. CHAKRAVARTHY
Keyword(s):  
Optimization Problem ◽  
Arrival Process ◽  
Single Server ◽  
Queueing Model ◽  
Process Map ◽  
Practical Applications ◽  
Setup Costs ◽  
Multiple Thresholds ◽  
Minimum Delay ◽  
Multi Server

We consider a multi-server queueing model in which arrivals occur according to a Markovian arrival process (MAP). There is a single-server and additional (backup) servers are added or removed depending on sets of thresholds. The service times are assumed to be exponential and the servers are assumed to be homogeneous. A comparison of this model to the classical MAP/M/c queueing model through an optimization problem yields some interesting results that are useful in practical applications. For example, we notice that positively correlated arrival process appears to benefit with the threshold type queueing model. We also give the minimum delay costs and the associated maximum setup costs so that the threshold type queueing model is to be preferred over the classical MAP/M/c model.

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.

A model for queues in series

1973 ◽  
Vol 10 (03) ◽  
pp. 691-696 ◽  
Author(s):  
O. P. Sharma
Keyword(s):  
Probability Distributions ◽  
Steady State Solution ◽  
Single Server ◽  
Poisson Input ◽  
Phase Type ◽  
In Series ◽  
Queues In Series ◽  
Finite Space ◽  
Multi Server ◽  
Stationary Behaviour

This paper studies the stationary behaviour of a finite space queueing model consisting of r queues in series with multi-server service facilities at each queue. Poisson input and exponential service times have been assumed. The model is suitable for phase-type service as well as service with waiting allowed before the different phases. In the case of single-server queues explicit expressions for certain probability distributions, parameters and a steady-state solution for infinite queueing space have been obtained.

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