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

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.

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Computing and Analysis of Multi Server Queueing Model Using Pentagonal Fuzzy Numbers

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/1099/1/012006 ◽

2021 ◽

Vol 1099 (1) ◽

pp. 012006

Author(s):

Mridula Jain ◽

Anamika Jain

Keyword(s):

Fuzzy Numbers ◽

Queueing Model ◽

Multi Server

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Queues with two units connected in series with a multiserver bulk service with accessible and non accessible batch in unit II

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v4n1.38 ◽

2014 ◽

Vol 4 (1) ◽

Author(s):

G. Ayyappan ◽

S. Velmurugan

Keyword(s):

Service Time ◽

Subject Classification ◽

Geometric Method ◽

Finite Buffer ◽

Queueing Model ◽

Service Station ◽

Matrix Geometric Method ◽

In Series ◽

Bulk Service ◽

Number Of Customers

This paper analyses a queueing model consisting of two units I and II connected in series, separated by a finite buffer of size N. Unit I has only one exponential server capable of serving customers one at a time. Unit II consists of c parallel exponential servers and they serve customers in groups according to the bulk service rule. This rule admits each batch served to have not less than ‘a’ and not more than ‘b’ customers such that the arriving customers can enter service station without affecting the service time if the size of the batch being served is less than ‘d’ ( a ≤ d ≤ b ). The steady stateprobability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained using the modified matrix-geometric method. Numerical results are also presented. AMS Subject Classification number: 60k25 and 65k30

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Optimal Management of Cloud Centers with Different Arrival Modes for Cloud Computing Environment

International Journal of Cloud Applications and Computing ◽

10.4018/ijcac.2012070104 ◽

2012 ◽

Vol 2 (3) ◽

pp. 86-97

Author(s):

Veena Goswami ◽

Sudhansu Shekhar Patra ◽

G. B. Mund

Keyword(s):

Cloud Computing ◽

Virtual Machines ◽

Service Level Agreement ◽

Service Level ◽

Finite Buffer ◽

Web Browser ◽

Computing Paradigm ◽

Computing Services ◽

Multi Server

Cloud computing is a new computing paradigm in which information and computing services can be accessed from a Web browser by clients. Understanding of the characteristics of computer service performance has become critical for service applications in cloud computing. For the commercial success of this new computing paradigm, the ability to deliver guaranteed Quality of Services (QoS) is crucial. Based on the Service level agreement, the requests are processed in the cloud centers in different modes. This paper analyzes a finite-buffer multi-server queuing system where client requests have two arrival modes. It is assumed that each arrival mode is serviced by one or more Virtual machines, and both the modes have equal probabilities of receiving service. Various performance measures are obtained and optimal cost policy is presented with numerical results. The genetic algorithm is employed to search the optimal values of various parameters for the system.

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

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595907001164 ◽

2007 ◽

Vol 24 (02) ◽

pp. 223-243 ◽

Cited By ~ 3

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.

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