Veena Goswami

Performance analysis of cloud with queue-dependent virtual machines

Cloud computing provides a new way for industries to meet the emerging business need for agility. Many public clouds are available for developers to build web applications on cloud. The process of entering into the cloud is generally in the form of a queue, so that each user need to wait until the current user is being served. In the system, each Cloud Computing User (CCU) requests Cloud Computing Service Provider (CCSP) for use of resources. If CCU finds the server busy, then the user has to wait till the current user completes the job. This may result in increase of queue length as well as waiting time, which may lead to request drop. To handle this problem, CCSP needs to find ways to reduce waiting time. We propose a finite multiserver queueing model with queue dependent heterogeneous servers where the web applications are modeled as queues and the virtual machines are modeled as service providers. CCSPs can use multiple servers and the number of busy servers changes depending on the queue length for reducing queue length and waiting time. This helps us to dynamically create and remove virtual machines in order to scaling up and down. We develop a recursive method to obtain the system steady-state probabilities. Various performance measures of the proposed scheme have been described and evaluated. Computational experiences in the form of graphs are presented.

Discrete-time bulk-service queues with accessible and non-accessible batches

This paper analyzes a discrete-time single-server infinite- (finite-) buffer bulk-service queues. The inter-arrival times of successive arrivals are assumed to be independent and geometrically distributed. The customers are served by a single-server in accessible or non-accessible batches. The service times of batches are also assumed to be independent and geometrically distributed. The steady-state probabilities with computational experiences have been presented.

Modeling and Analysis of Discrete-Time Multiserver Queues with Batch Arrivals: GIX/Geom/m

Multiserver queues are often encountered in telecommunication systems and have special importance in the design of ATM networks. This paper analyzes a discrete-time multiserver queueing system with batch arrivals in which the interbatch and service times are, respectively, arbitrarily and geometrically distributed. Using supplementary-variable and embedded-Markov-chain techniques, the queue is analyzed only for the early arrival system. Since the late arrival system can be discussed similarly, it is not considered here. In addition to developing relations among state probabilities at prearrival, arbitrary, and outside observers observation epochs, the numerical evaluation of state probabilities is also discussed. It is also shown that, in the limiting case, the relations developed here tend to continuous-time counterparts. Further, the waiting-time distribution of a random customer of a batch is obtained. Finally, in some cases simulation experiments have been performed to validate our results.

Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed.

Analysis of discrete-time batch service renewal input queue with multiple working vacations

This paper investigates a discrete-time single server batch service queue with multiple working vacations wherein arrivals occur according to a discrete-time renewal process. The server works with a different service rate rather than completely stopping during the vacation period. The service is performed in batches and the server takes a vacation when the system does not have any waiting customers at a service completion epoch or a vacation completion epoch. We present a recursive method, using the supplementary variable technique to obtain the steady-state queue-length distributions at pre-arrival, arbitrary and outside observers observation epochs. The displacement operator method is used to solve simultaneous non-homogeneous difference equations. Some performance measures and waiting-time distribution in the system have also been discussed. Finally, numerical results showing the effect of model parameters on key performance measures are presented.

On discrete-time multiserver queues with finite buffer: GI/Geom/ m/N

Multiserver queues are often encountered in telecommunications systems and have special importance in the design of asynchronous transfer mode network. This paper analyzes a discrete-time multiserver queueing system with finite buffer in which the interarrival and service times are, respectively, arbitrarily and geometrically distributed. Using supplementary variable and imbedded Markov-chain techniques, the queue is analyzed for the early arrival system. Besides, developing relations among state probabilities at prearrival, arbitrary and outside observers observation epochs, the waiting-time analysis is also carried out.

Analysis of discrete-time multi-server queue with balking

This paper analyses a discrete-time multi-server queue with balking behavior. The inter-arrival and service times are assumed to be independent and geometrically distributed. If all the servers are busy, an arriving customer either enters with probability b or balks with probability 1 − b. Otherwise, the service of the arriving customer commences immediately. The system is analysed under the assumptions of an early arrival system and a late arrival system with delayed access. Closed-form expressions for the steady-state probabilities at arbitrary epochs and an outside observers observation epoch probabilities are obtained. Various performance measures along with some numerical results in the form of a table and graphs are presented. Some special cases of the model have also been discussed. We have shown that the obtained results converge to the results of the continuous-time counterparts in the limiting case.

Analysis of finite-buffer discrete-time batch-service queue with batch-size-dependent service☆

Abstract Over the last two decades there has been considerable growth in digital communication systems which operate on a slotted system. In several applications, transmission of packets over the network takes place in batches of varying size, and transmission time depends upon the size of the batch. Performance modelling of these systems is usually done using discrete-time queues. In view of this, we consider a single-server queue with finite-buffer in a discrete-time domain where the packets are transmitted in batches (of varying size) according to minimum and maximum threshold limit, usually known as general batch service rule. The transmission time (in number of slots) of these batches depends on the number of packets within the batch under transmission, and is arbitrarily distributed. We obtain, in steady-state, distribution of the number of packets waiting in the queue and in service (those being transmitted in batches). In addition, we also obtain average number of packets waiting in queue, in the system, with the server, rejection probabilities, etc. Finally, computational experiences with a variety of numerical results have been discussed by introducing a cost model which gives optimum value of the lower threshold limit.

Analysis of Discrete-Time Single Server Queue with Balking and Multiple Working Vacations

Abstract This paper analyzes a discrete-time single server queueing system with balking and multiple working vacations. The arriving customers balk (that is, do not join the queue) with a probability. The inter-arrival times of customers are assumed to be independent and geometrically distributed. The server works at a different rate rather than completely stopping service during vacations. The service times during a service period, service times during a vacation period and vacation times are assumed to be geometrically distributed. We obtain the closed form expressions for the steady-state probabilities at arbitrary and outside observer’s observation epochs. Computational experiences with a variety of numerical results are discussed in the form of tables and graphs. Moreover, some queueing models discussed in the literature are derived as special cases of our model.

Performance Analysis of Cloud Computing Centers for Bulk Services

Cloud is a service oriented platform where all kinds of virtual resources are treated as services to users. Several cloud service providers have offered different capabilities for a variety of market segments over the past few years. The most important aspects of cloud computing are resource scheduling, performance measures, and user requests. Sluggish access to data, applications, and web pages spoils employees and customers alike, as well as cause application crashes and data losses. In this paper, the authors propose an analytical queuing model for performance evaluation of cloud server farms for processing bulk data. Some important performance measures such as mean number of tasks in the queue, blocking probability, and probability of immediate service, and waiting-time distribution in the system have also been discussed. Finally, a variety of numerical results showing the effect of model parameters on key performance measures are presented.