On transient queue-size distribution in the batch arrival system with the N-policy and setup times

In the paper the $M^{X}/G/1$ queueing system with the $N$-policy and setup times is considered. An explicit formula for the Laplace transform of the transient queue-size distribution is derived using the approach consisting of few steps. Firstly, a "special\u27\u27 modification of the original system is investigated and, using the formula of total probability, the analysis is reduced to the case of the corresponding system without limitation in the service. Next, a renewal process generated by successive busy cycles is used to obtain the general result. Sample numerical computations illustrating theoretical results are attached as well

A study of some M[x]/G/1 type queues with random breakdowns and bernouilli schedule server vacations based on a single vacation policy

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Queueing systems arise in modelling of many practical applications related to computer sciences, telecommunication networks, manufacturing and production, human computer interaction, and so on. The classical queueing system, even vacation queues or queues subject to breakdown, might not be sufficiently realistic. The purpose of this research is to extend the work done on vacation queues and on unreliable queues by studying queueing systems which take into consideration both phenomena. We study the behavior of a batch arrival queueing system with a single server, where the system is subject to random breakdowns which require a repair process, and on the other hand, the server is allowed to take a vacation after finishing a service. The breakdowns are assumed to occur while serving a customer, and when the system breaks down, it enters a repair process immediately while the customer whose service is interrupted comes back to the head of the queue waiting for the service to resume. Server vacations are assumed to follow a Bernoulli schedule under single vacation policy. We consider the above assumptions for different queueing models: queues with generalized service time, queues with two-stages of heterogeneous service, queues with a second optional service, and queues with two types of service. For all the models mentioned above, it is assumed that the service times, vacation times, and repair times all have general arbitrary distributions. Applying the supplementary variable technique, we obtain probability generating functions of queue size at a random epoch for different states of the system, and some performance measures such as the mean queue length, mean waiting time in the queue, proportion of server's idle time, and the utilization factor. The results obtained in this research, show the effect of vacation and breakdown parameters upon main performance measures of interest. These effects are also illustrated using some numerical examples and graphs.This work is funded by the Ministry of Education, Kingdom of Bahrain

Discrete events: Perspectives from system theory

Systems Theory;differentiaal/ integraal-vergelijkingen

Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations.

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Online learning and decision-making from implicit feedback

This thesis focuses on designing learning and control algorithms for emerging resource allocation platforms like recommender systems, 5G wireless networks, and online marketplaces. These systems have an environment which is only partially known. Thus, the controllers need to make resource allocation decisions based on implicit feedback obtained from the environment based on past actions. The goal is to sequentially select actions using incremental feedback so as to optimize performance while simultaneously learning about the environment. We study three problems which exemplify this setting. The first is an inference problem which requires identification of sponsored content in recommender systems. Specifically, we ask if it is possible to detect the existence of sponsored content disguised as genuine recommendations using implicit feedback from a subset of users of the recommender system. The second problem is the design of scheduling algorithms for switch networks when the user-server link statistics are unknown (for e.g., in wireless networks, online marketplaces). The scheduling algorithm has to tradeoff between scheduling the optimal links and obtaining sufficient feedback about all the links for accurate estimates. We observe the close connection of this problem to the stochastic multi-armed bandit problem and analyze bandit-style explore-exploit algorithms for learning the statistical parameters while simultaneously assigning servers to users. The third is the joint problem of base station activation and rate allocation in an energy efficient wireless network when the channel statistics are unknown. The controller observes instantaneous channel rates of activated BSs, and thereby sequentially obtains implicit feedback about the channel. Here again, there is a tradeoff between learning the channel versus optimizing the operation cost based on estimated parameters. For each of these systems, we propose algorithms with provable asymptotic guarantees. These learning algorithms highlight the use of implicit feedback in online decision making and control.Electrical and Computer Engineerin