Mean Number Of Jobs Research Articles

An efficient performance evaluation model for the resource clusters in cloud environment using continuous time Markov chain and Poisson process

Cloud computing enables us to share the jobs across various cloud data centers with the internet as a backbone in order to process the jobs. The selections of the data centers to process the jobs are based on the potential of the data centers, arrival rate of the jobs and better resource utilization. Performance modeling and evaluation of the cloud systems shows a perfect picture of probability of distribution of jobs among the datacenters, mean number of jobs in the datacenters and makespan of the cloud environment. In order to provide a best performance evaluation model which leads to a prosperous cloud environment the proposed approach calculates the arrival rate of jobs using Poisson process in which the arrival rate can be calculated for infinite time intervals and the mean number of jobs and also the resource utilization are modeled using continuous Markov chain. The problems related to the calculation of arrival rate and resource utilization model of the existing approaches are solved to enhance the job scheduling by minimizing the makespan of the cloud environment.

Performance analysis of cognitive radio networks under spectrum sharing using queuing approach

Cognitive radio is considered to be an emerging technology that provides a platform to share the spectrum between primary and secondary users. As a result, the quality of service and the network usage is bound to improve. In order to evaluate the performance of such a system queuing theory can be considered as an important tool. In the aforementioned context, the central focus of this work is on evaluating and analyzing the network performance using queuing approach. This approach uses the Dimensional Reduction Scheme to reduce the dimension of the Markov chain and the matrix-analytic method for calculating the stationary probabilities. The performance of the system is evaluated on four performance measures namely, utilization, mean response time, mean number of jobs and waiting time. The simulation results show that the performance of the system is satisfactory when primary and secondary users share the network.

Characterizing MEGACO Security in the presence Diameter Server

This paper analyzes performance of MEGACO (Media Gateway Control Protocol) based on Diameter which is an Authentication, Authorization,andAccounting (AAA) protocol developed within the Internet Engineering Task Force(IETF).Diameter is loosely based on Remote Authentication Dial In User Service (RADIUS), which has previously been used to provide AAA services for dial-up and terminal server access environments. An analytical model is provided for the performance of a MEGACO network while there is a Diameter server to guarantee Authentication in call flow. Ultimately, the M/M/c and M/D/c traffic models are provided to evaluate QoS (Quality of Service) in the call flow and some of the key performance benchmarks response time to process the MEGACO calls and mean number of jobs in the system when there is security mechanism is studied.

Comparative Study of M/Er/1 and M/M/1 Queuing Delay Models of the two IP-PBXs

Voice over Internet Protocol (VoIP) is a general term for a family of transmission technologies to delivery of voice communications over IP networks such as the Internet or other packet-switched networks. VoIP systems employ session control protocols to control the set-up and tear-down of calls as well as audio codecs which encode speech allowing transmission over an IP network as digital audio via an audio stream. This paper analyzes performance of SIP model (Session Initiation Protocol) based on IPPBX (IP-Private Branch exchange) which is a software application which provides call routing services by parsing and forwarding all the incoming SIP packets in various remote IP telephony network. Then, the M/Er/1 and M/M/1 performance models of the IP-PBX was simulated and some of the key performance benchmarks such as average response time to process the SIP calls and mean number of jobs in the system was reviewed.

Optimal control of servers in front and back rooms with correlated work

In this article we deal with the problem of optimal server allocation between the front and the back room of a service facility (for all states of the system) when the work in the back room is generated by the service provided in the front room. The servers are cross-trained and can switch between front room and back room tasks without any loss of productivity. We also determine the optimal number of servers required to meet certain service levels. Our service criteria is that both the mean number of customers waiting for service in the front room and the mean number of jobs (work) accumulated are bounded from above. We model the problem as a Markov decision problem and use linear programming to solve it.

Closed polling models with failing nodes

Closed polling systems with station breakdowns, under the gated, exhaustive or globally gated services regimes, are studied and analyzed. Multi-dimensional sets of probability generating functions of the system’s state are derived. They are further utilized to obtain an approximate solution for the mean number of jobs residing in the system’s various queues at polling instants. The analysis is then concentrated on the case of cyclic Bernoulli polling. Explicit formulae for the mean number of jobs, as well as for the expected cycle duration and system utilization, are derived. Comparison of the throughputs of the three regimes concludes the paper.

Exact solutions for networks of queues with blocking-after-service

The paper has two major parts. The first part deals with two-station networks with blocking-after-service (BAS) mechanism and different station types. In this part only single class of jobs is allowed. The contribution here is to show that exact solutions exist for two-station queueing networks with BAS mechanism having different station types. The exact equilibrium state probability distributions are derived. Insensitivity is investigated and formulas for performance measures are obtained. It is demonstrated that the throughput, mean number of jobs and mean number of Cblocked jobs depend on the scheduling discipline. A queueing network model with more than two stations is analyzed in the second part. Multiple-job classes with job class change, and different station types are allowed in the model. Exact solutions for equilibrium state probabilities and performance measures are obtained under the condition that only a certain total number of jobs is allowed in the network.

Exact analysis of queueing networks with multiple job classes and blocking-after-service

Two models of closed queueing networks with blocking-after-service and multiple job classes are analyzed. The first model is a network withN stations and each station has either type II or type III. The second model is a star-like queueing network, also called a central server model, in which the stations may have either type I or type IV, with the condition that the neighbors of these stations must be of type II or type III such that blocking will be caused only by this set of station types. Exact product form solutions are obtained for the equilibrium state probabilities in both models. Formulae for performance measures such as throughput and the mean number of jobs are also derived.

Diabetes mellitus and employment: is there discrimination in the workplace?

The employment record of 102 diabetic workers (73 men, 29 women), identified in a cross-sectional survey of 5670 middle-aged people in a New Zealand workforce, was studied for evidence of discrimination in the workplace. Compared with 403 matched controls (292 men, 111 women), diabetic workers showed no significant differences in socioeconomic status, educational attainment, or distribution between occupational groups. Similarly, mean duration of current employment (12.3 vs 12.4 years), mean number of jobs in the past 5 years (1.25 vs 1.34 jobs), frequency of sickness absence, and mean number of hours worked each week (43.5 vs 43.3h) did not differ significantly between diabetic and non-diabetic groups. We found no significant differences in work stress, even among those diabetic individuals with poor blood glucose control. There was no convincing evidence across a broad spectrum of industry that diabetic workers did suffer discrimination in the workplace.

Two parallel processors with coupled inputs

We consider the double queue arising from a system consisting of two processors serving three job streams generated by independent Poisson sources. The central job stream of rate v consists of jobs which place resource demands on both processors, which are handled separately by each processor once the request is made. In addition, the first processor receives background work at a rate of λwhile the second receives similar tasks at a rate η. Each processor has exponentially distributed service times with rates α and β respectively. A functional equation is found for P(z, w), the generating function of the joint queue-length distribution, which leads to a relation between P(z, 0) and P(0, w) in the region |z|, |w| < 1 of a complex algebraic curve associated with the problem. The curve is parametrized by elliptic functions z(ξ) and w(ξ) and the relation between Ρ (z(ξ), 0) and P(0, w(ξ)) persists on their analytic continuation as elliptic functions in the ξ-plane. This leads to their eventual determination by an appeal to the theory of elliptic functions. From this determination we obtain asymptotic limit laws for the expectations of the mean number of jobs in each queue conditioned on the other, as the number of jobs in both processors tends to∞. Transitions are observed in the asymptotic behavior of these quantities as one crosses various boundaries in the parameter space. An interpretation of these results via the theory of large deviations is presented.

Moment analysis for load-dependent mixed product form queueing networks

A solution algorithm is developed for higher moments of the number of jobs at the stations in load-dependent mixed product form queuing networks. Such networks are important because they can be used to model computer systems and computer communication networks. A relationship is proved and applied between the derivatives of these moments and higher moments. The derivative measures are calculated using a mean value analysis type algorithm called moment analysis. The authors describe the model and review the product form solutions for load-dependent mixed queuing networks. They develop the moment analysis algorithm and the formulas for the performance measures such as the response time, throughput and mean number of jobs in the stations. The complexity of the algorithm is discussed. >

Asymptotic analysis of a large closed queueing network with discriminatory processor sharing

In this paper the steady-state behavior of a closed queueing network with multiple classes and large populations is investigated. One of the two nodes of the network simply introduces random delays and the discipline in the other node is discriminatory processor sharing. The network is not product-form, so not even the steady-state behavior is known. We assume that the usage is moderately heavy, and obtain two-term asymptotic approximations to the mean number of jobs, and the mean sojourn time, of each class of jobs in the processor node. We also obtain the leading term in the asymptotic approximation to the joint distribution of the number of jobs in the processor node, which is a zero-mean multivariate Gaussian distribution around a line through the origin.

Computational algorithms for networks of queues with rejection blocking

Open, closed and mixed queueing networks with reversible routing, multiple job classes and rejection blocking are investigated. In rejection blocking networks blocking event occurs when upon completion of its service of a particular station's server, a job attempts to proceed to its next station. If, at that moment, its destination station is full, the job is rejected. The job goes back to the server of the source station and immediately receives a new service. This is repeated until the next station releases a job and a place becomes available. In the model jobs may change their class membership and general service time distributions depending on the job class are allowed. Two station types are considered: Either the scheduling discipline is symmetric, in which case the service time distributions are allowed to be general and dependent on the job class or the service time distributions at a station are all identical exponential distributions, in which case more general scheduling disciplines are allowed. An exact product form solution for equilibrium state probabilities is presented. Using the exact product form solution of the equilibrium state distribution, algorithms for computation of performance measures, such as mean number of jobs and throughputs, are derived. The complexity of the algorithms is discussed.

Analysis of catastrophic phenomena in a multiprogramming system

AbstractThis paper presents a state analysis of multiprogramming, using the concept of cusp catastrophe in the theory of catastrophe. Based on the result, the catastrophic phenomena in the multiprogramming system are analyzed. It is shown first that the multiprogramming system exhibits two stable states, i.e., monostable and bistable states, for the change of job generation rate and the change of the maximum multiprogramming level. Then it is shown that a rapid change (catastrophe) of the performance of the multiprogramming system, such as the mean number of jobs in the system, throughput and response time, may occur with the change of the stable state of the system. Furthermore, it is shown that for any given job generation rate, there exists a maximum multiprogramming level which maximizes the throughput and minimizes the response time.

Modifying Job Sequencing Rules for Work-in-Process Inventory Reduction

Abstract In most reported studies of job dispatching rules the primary criterion for evaluating alternative rules has been the mean number of jobs in the shop, or the equivalent. This paper argues that the mean value of jobs in the shop is a more generally useful measure because it is a determinant of work-in-process (WIP) inventory carrying cost. For certain simple single-server systems the shortest processing time rule (SPT) is known to be optimal on the first criterion. A value-weighted version of SPT, termed SWPT, is optimal on the second criterion (mean value). We show by means of a simulation study that introduction of a similar dollar-weighting feature into more complex rules is effective in reducing mean WIP inventory, even in complex multimachine stochastic systems. Since our suggested dispatch rule modifications require value weighting, correct valuation of jobs is essential. The subject of how to determine the value of a job dynamically as it moves through the shop is discussed.