A Queueing Network Model for Performance Prediction of Apache Cassandra

NoSQL databases such as Apache Cassandra have attracted large interest in recent years thanks to their high availability, scalability, flexibility and low latency. Still there is limited research work on performance engineering methods for NoSQL databases, which yet are needed since these systems are highly distributed and thus can incur significant cost/performance trade-offs. To address this need, we propose a novel queueing network model for the Cassandra NoSQL database aimed at supporting resource provisioning. The model defines explicitly key configuration parameters of Cassandra such as consistency levels and replication factor, allowing engineers to compare alternative system setups. Experimental results based on the YCSB benchmark indicate that, with a small amount of training for the estimation of its input param- eters, the proposed model achieves good predictive accuracy across different loads and consistency levels. The average performance errors of the model compared to the real results are between 6% and 10%. We also demonstrate the applicability of our model to other NoSQL databases and other possible utilisation of it

On M/G/1 system under NT policies with breakdowns, startup and closedown

AbstractThis paper studies the vacation policies of an M/G/1 queueing system with server breakdowns, startup and closedown times, in which the length of the vacation period is controlled either by the number of arrivals during the vacation period, or by a timer. After all the customers are served in the queue exhaustively, the server is shutdown (deactivates) by a closedown time. At the end of the shutdown time, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the closedown time. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. If some customers arrive during this closedown time, the service is immediately started without leaving for a vacation and without a startup time. We analyze the system characteristics for each scheme

The departure process of a quorum queueing system

AbstractWe study in this paper the departure process of a bulk service queueing system. The server operates under a minimum batch size strategy. We characterize the departure process through the distribution of the interdeparture times of batches and of customers, the distribution of the number of customers in a batch, and the coefficient of correlation between the interdeparture time of a batch and the number of customers in the batch. A numerical illustration is presented

The Mx/G/1 Queue with Unreliable Server, Delayed Repairs, and Bernoulli Vacation Schedule under T-Policy

In this paper we study a batch arrival queuing system. The server may break down while delivering service. However, repair is not provided immediately, rather it is delayed for a random amount of time. At the end of service, the server may process the next customer if any are available, or may take a vacation to execute some other job. Finally, the server implements the T-policy. We describe for this system an optimal management policy. Numerical examples are provided

Analysis of Single Server Fixed Batch Service Queueing System under Multiple Vacation with Catastrophe

Consider a single server fixed batch service queueing system under multiple vacation with a possibility of catastrophe in which the arrival rate ? follows a Poisson process and the service time follows an exponential distribution with parameter ?. Further we assume that the catastrophe occur at the rate of ? which follows a Poisson process and the length of time the server in vacation follows an exponential distribution with parameter ?.  Assume that the system initially contains k customers when the server enters in to the system and starts the service immediately in a batch of size k. After completion of a service, if he finds less than k customers in the queue, then the server goes for a multiple vacation of length ?. If there are more than k customers in the queue then the first k customers will be selected from the queue and service will be given as a batch. We are analyzing the possibility of catastrophe that is whenever a catastrophe occurs in the system, all the customers who are in the system will be completely destroyed and system becomes an empty and server goes for a multiple vacation. This model is completely solved by constructing the generating function  and we have derived the closed form solutions for probability of number of customers in the queue during the server busy and in vacation. Further we are providing the analytical solution for mean number of customers and variance of the system. Numerical studies have been done for analysis of mean and variance of number of customers in the system for various values of ?, µ, ? and k and also various particular cases of this model have been discussed. Keywords: Single server queue , Fixed batch service , Catastrophe, Multiple vacation, Steady state distributio

Batch arrival bulk service queue with unreliable server, second optional service, two different vacations and restricted admissibility policy

This paper is concerned with batch arrival queue with an additional second optional service to a batch of customers with dissimilar service rate where the idea of restricted admissibility of arriving batch of customers is also introduced. The server may take two different vacations (i) Emergency vacation-during service the server may go for vacation to an emergency call and after completion of the vacation, the server continues the remaining service to a batch of customers. (ii) Bernoulli vacation-after completion of first essential or second optional service, the server may take a vacation or may remain in the system to serve the next unit, if any. While the server is functioning with first essential or second optional service, it may break off for a short period of time. As a result of breakdown, a batch of customers, either in first essential or second optional service is interrupted. The service channel will be sent to repair process immediately. The repair process presumed to be general distribution. Here, we assumed that the customers just being served before server breakdown wait for the server to complete its remaining service after the completion of the repair process. We derived the queue size distribution at a random epoch and at a departure epoch under the steady state condition. Moreover, various system performance measures, the mean queue size and the average waiting time in the queue have been obtained explicitly. Some particular cases and special cases are determined. A numerical result is also introduced

Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain. We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved