IJERT-Distribution of Occupied Resources on A Discrete Resources Sharing in A Queueing System (original) (raw)
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Distribution of Occupied Resources on A Discrete Resources Sharing in A Queueing System
International Journal of Engineering Research and, 2021
In this paper, we study discrete resources sharing in a queueing system. We build analytical model of the distribution of occupied resources that can help for resources dimensioning. Both infinite and finite amount of discrete server resources are highlighted and validated with special cases of individual resource requirement following Poisson and Binomial distribution. It is found that there is a peak of usage near the average number of resources requested by customers, and other small peaks with low probability at multiples of this mean. The charging factor of the queue impacts mostly on the resources occupation distribution.
RUDN Journal of Mathematics, Information Sciences and Physics
The mathematical model of the system, that consists of a storage device and several homogeneous servers and operates in a random environment, and provides incoming applications not only services, but also access to resources of the system, is being constructed. The random environment is represented by two independent Markov processes. The first of Markov processes controls the incoming flow of applications to the system and the size of resources required by each application. The incoming flow is a Poisson one, the rate of the flow and the amount of resources required for the application are determined by the state of the external Markov process. The service time for applications on servers is exponential distributed. The service rate and the maximum amount of system resources are determined by the state of the second external Markov process. When the application leaves the system, its resources are returned to the system. In the system under consideration, there may be failures in accepting incoming applications due to a lack of resources, as well as loss of the applications already accepted in the system, when the state of the external Markov process controlling the service and provision of resources changes. A random process describing the functioning of this system is constructed. The system of equations for the stationary probability distribution of the constructed random process is presented in scalar form. The main tasks for further research are formulated.
International Journal of Mathematics and Mathematical Sciences, 1992
This paper introduces a bulk queucing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the qucueing level is less than r the server idles until the queue accumulates r customers in total.
Discrete-time queues with variable service capacity: a basic model and its analysis
Annals of Operations Research, 2013
In this paper, we present a basic discrete-time queueing model whereby the service process is decomposed in two (variable) components: the demand of each customer, expressed in a number of work units needed to provide full service of the customer, and the capacity of the server, i.e., the number of work units that the service facility is able to perform per time unit. The model is closely related to multi-server queueing models with server interruptions, in the sense that the service facility is able to deliver more than one unit of work per time unit, and that the number of work units that can be executed per time unit is not constant over time. Although multi-server queueing models with server interruptions-to some extentallow us to study the concept of variable capacity, these models have a major disadvantage. The models are notoriously hard to analyze and even when explicit expressions are obtained, these contain various unknown probabilities that have to be calculated numerically, which makes the expressions difficult to interpret. For the model in this paper, on the other hand, we are able to obtain explicit closed-form expressions for the main performance measures of interest. Possible applications of this type of queueing model are numerous: the variable service capacity could model variable available bandwidths in communication networks, a varying production capacity in factories, a variable number of workers in an HR-environment, varying capacity in road traffic, etc.
In this paper, a discrete-time single server queueing system with infinite buffer size and geometrically distributed arrivals is considered. We derive the functional equations and analyze the distribution of the number of customers served during a busy period for geometrically distributed service time as well as for deterministic service time. We also show that in the limiting case the results obtained in this paper are consistent with the corresponding continuous-time counterparts by Medhi [1].
Queueing Systems with Random Volume Customers and their Performance Characteristics
Journal of information and organizational sciences, 2021
In the paper, we consider non-classical queueing systems with non-homogeneous customers. The non-homogeneity we treat in the following sense: in systems under consideration, we characterize each customer by random capacity (volume) that can have an influence on his service time. We analyze a stochastic process having the sense of the total volume of all customers present in the system at given time instant. Such analysis for different queueing systems with unlimited or limited total volume can be used in designing of nodes of computer and communication networks while determining their buffer space capacity. We discuss basic problems of the theory of these systems and their performance characteristics. We also present some examples and results for systems with random volume customers
There are three topics in the thesis. In the first topic, we addressed a control problem for a queueing system, known as the "N-system", under the Halfin-Whitt heavy traffic regime and a static priority policy was proposed and is shown to be asymptotically optimal, using weak convergence techniques. In the second topic, we focused on the hospitals, where faster servers(nurses), though work more efficiently, have the heavier workload, and the Randomized Most-Idle (RMI) routing policy was proposed to tackle this unfairness issue, trying to reward faster servers who serve more with less workload. we extended the existing result to show that this desirable property of the RMI policy holds under a system with multiple customer classes using theoretical exact analysis as well as numerical simulations. In the third topic, the problem was to decide an appropriate number of representatives over time according to the prescribed service quality level in the call center. We examined the stability of two methods which were designed to generate appropriate staffing functions on a simulated data and real call center data from an actual bank.
2016
Queueing Theory is one of the most commonly used mathematical tool for the performance evaluation of systems. The aim of the book is to present the basic methods, approaches in a Markovian level for the analysis of not too complicated systems. The main purpose is to understand how models could be constructed and how to analyze them. It is intended not only for students of computer science, engineering, operation research, mathematics but also those who study at business, management and planning departments, too. It covers more than one semester and has been tested by graduate students at Debrecen University over the years. It gives a very detailed analysis of the involved queueing systems by giving density function, distribution function, generating function, Laplace-transform, respectively. Furthermore, Java-applets are provided to calculate the main performance measures immediately by using the pdf version of the book in a WWW environment. I have attempted to provide examples for ...
The Discrete-Time Queue with Geometrically Distributed Service Capacities Revisited
Springer eBooks, 2013
We analyze a discrete-time queue with variable service capacity, such that the total amount of work that can be performed during each time slot is a stochastic variable that is geometrically distributed. We study the buffer occupancy by constructing an analogous model with fixed service capacity. In contrast with classical discrete-time queueing models, however, the service times in the fixed-capacity model can take the value zero with positive probability (service times are non-negative). We study the late arrival models with immediate and delayed access, the first model being the most natural model for a system with fixed capacity and non-negative service times and the second model the more practically relevant model for the variable-capacity model.