Controllable Arrival Rates Research Articles

A Finite Capacity Finite Source Single Server Markovian Queueing System with Discouraged Arrivals Retention of Reneged Customers and Controllable Arrival Rates with Feedback

A Finite Capacity Finite Source Single Server Markovian Queueing System with Discouraged Arrivals Retention of Reneged Customers and Controllable Arrival Rates with Feedback

An Infinite Capacity Single Server Markovian Queueing System With Discouraged Arrivals Retention Of Reneged Customers and Controllable Arrival Rates With Feedback

An Infinite Capacity Single Server Markovian Queueing System With Discouraged Arrivals Retention Of Reneged Customers and Controllable Arrival Rates With Feedback

M/M/1 Interdependent Queuing Model with Vacation and Controllable Arrival Rates

Objectives: Rather than working nonstop in the service area, servers take vacations when they have no clients. To determine the probability and features of the queuing system, this study introduces controllable arrival rates and interdependency in the system's service and arrival processes. It also performs a numerical verification of the results. Methods: A recursive method is employed to solve the steady-state probability equations, yielding explicit iterative formulas under the assumption that a single server provides services to all clients. Here, customer arrivals are controlled as either faster or slower, with Poisson assumed by default. Findings: For this model, steady-state solutions and characteristics are derived and explored, and some numerical analysis is carried out using MATLAB. All the probabilities are expressed in terms of , which indicates the system when empty. The movement of the average number of customers in the system and the expected waiting time, and respectively, of the customers in the system is investigated through a graph. and decrease when dependence service rate, and faster arrival rate increase. Additionally, increases and decreases when the slower arrival rate increases. Novelty: Although there have been studies on vacation in queuing theory, this new approach aims to bridge the gap between vacation and interdependency in the arrival and service process, as well as controllable arrival rates. When vacations with predictable arrival rates are utilised advantageously for the benefit of both the server and the client, waiting times may be minimised and the most practical, economical service can be provided. Keywords: Markovian Queuing System, Vacation, Loss and Delay, Finite Capacity, Interdependent Arrival and Service Rates, Varying Arrival Rates, Bivariate Poisson Process

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

Objectives: This study aims at (i) introducing the finite capacity of the interdependent queueing model with breakdown and controllable arrival rates, (ii) calculating the average number of clients in the system, and identifying the expected waiting period of the clients in the system, (iii) dealing with the model descriptions, steady-state equations, and characteristics, which are expressed in terms of , and (iv) analyzing the probabilities of the queueing system and its characteristics with numerical verification of the obtained results. Methods: While providing the input, the arrival rates through faster and slower arrival rates are controlled using the Poisson process. Also, the service provides an exponential distribution. The server provides the service on an FCFS basis. In this article, two types of models are used: and which are the system’s conditions, where represents the number of units present in the queue in which their probability is and . All probabilities are distributed based on the speed of advent using this concept. Then, the steady-state probabilities are computed using a recursive approach. Findings: This paper discovers the number of clients using the system on average and the expected number of clients in the system using the probability of the steady-state calculation. Little’s formula is used to derive the expected waiting period of the clients in the system. Novelty: There are articles connected to the finite capacity of failed service in functioning and malfunctioning, but this takes the initiative to provide a link in connection with the rates of the controllable arrivals and interdependency in the arrival and service processes. Mathematics Subject allocation: 60K25, 68M20, 90B22. Keywords: M/M/1/K Queue Model, Finite Capacity, Breakdown, Controllable Arrival rates, FCFS Queue Discipline

M/M/1/K Loss and Delay Interdependent Queueing Model with Vacation and Controllable Arrival Rates

Objectives: In this study, we assume that the vacation is taken while there are no consumers in the queue. There are several servicemen who will take the synchronous multiple vacations in the system. Methods: Assumed some loss and delay in consumers (Elective and emergency) and solve the steady-state probability equations using recursive approach and acquired some obvious iterative expressions. Findings: Carried out some numerical analysis using MATLAB and investigated the movement of , , and through graph. Further, , , and increase when increases; decrease when M increases. Additionally, when L increases remains constant and increase. Novelty: Expanded the preceding models in this study by including vacations and performing the numerical analysis. Using vacation with controllable arrival rates in an optimal way in order to benefit both the server and the customer will minimise waiting time and provide the most feasible, affordable service to the consumer. Keywords: Markovian Queueing System, Vacation, Loss and Delay, Finite Capacity, Interdependent Arrival and Service Rates, Varying Arrival Rates, Bivariate Poisson Process

INVESTIGATION OF N-POLICY MARKOVIAN QUEUEING SYSTEM WITH DESPONDENT ARRIVALS, RETAINMENT OF RENEGED CUSTOMERS AND CONTROLLABLE ARRIVAL RATES

Afinite capacity, finite source, Markovian queueing model with despondent arrivals, retainment of reneged customers and controllable arrival rates is considered. Using this model, a steady-state solution and system characteristics can be obtained. The measures of effectiveness of the queueing model are also derived. Numerical results are given for better understanding and relevant conclusion is presented.

English

English

M/M/c/N/K Loss and Delay Interdependent Queueing Model with Controllable Arrival Rates and Reverse Balking

M/M/c/N/K Loss and Delay Interdependent Queueing Model with Controllable Arrival Rates and Reverse Balking

M/M/2/k Loss and Delay Interdependent Queueing Model with Controllable Arrival Rates, No Passing and Feedback

M/M/2/k Loss and Delay Interdependent Queueing Model with Controllable Arrival Rates, No Passing and Feedback

A multi server markovian queueing system with discouraged arrivals, retention of reneged customers, controllable arrival rates, loss and delay and no passing

A multi server markovian queueing system with discouraged arrivals, retention of reneged customers, controllable arrival rates, loss and delay and no passing

A finite capacity multiserver interdependent retrial queueing model with controllable arrival rates

We consider a finite capacity interdependent retrial queueing model with controllable arrival rates, when c = 1,2. The steady state solution and system characteristics are derived for this model. The analytical results are numerically illustrated. Mathematics Subject Classification: 60K25; 68M20; 90B22

The M/M/1/K interdependent retrial queueing model with impatient customers and controllable arrival rates

In this paper an M/M/1/K interdependent retrial queueing model with controllable arrival rates and impatient customers is considered. The steady state solutions and the system characteristics are derived for this model. The analytical results are numerically illustrated and the effect of the nodal parameters on the system characteristics are studied and relevant conclusion is presented. Keywords: finite capacity, interdependent primary arrival and service processes, impatient customers, retrial queue, single server.

Optimal arrival rate and service rate control of multi-server queues

We consider the problem of optimal control of a multi-server queue with controllable arrival and service rates. This study is motivated by its potential application to the design and control of data centers. The cost structure includes customer holding cost which is a non-decreasing convex function of the number of customers in the system, server operating cost which is a non-decreasing convex function of the chosen service rate, and system operating reward which is a non-decreasing concave function of the chosen arrival rate. We formulate the problem as a continuous-time Markov decision process and derive structural properties of the optimal control policies under both discounted cost and average cost criterions.

Investigation of Probability Generating Function in an Interdependent <i>M/M/</i>1:(∞; GD) Queueing Model with Controllable Arrival Rates Using Rouche’s Theorem

Present paper deals a M/M/1:(∞; GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration; which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.

M/M/c/K loss and delay interdependent queueing model with controllable arrival rates and no passing

In this paper a finite capacity, loss and delay, interdependent queueing system with controllable arrival rates and no passing has been considered. For this model, the steady state probabilities are derived and the average waiting times for the two types of customers (elective and emergency) are obtained for varying arrival rates when the arrival and service processes are interdependent. Numerical examples are given for a better understanding.

The M/Ma.b/C interdependent queueing model with controllable arrival rates

In this paper we introduce an M/Ma.b/C interdependent queueing model with controllable arrival rates. The steady state solutions and the system characteristics are derived and analysed for this model. It is observed that the mean dependence rate between the arrival and service processes can reduce the congestion in queues and delays in transmission. This is the most general model which includes most of the earlier models as particular cases for specific or limiting values of the parameters. The tabulation values help to control the queue length with the suitable selection of the parameters. The graphical figures help us to select the optimal values of the parameters to control the queue length. As an illustration, if the faster arrival rates are increasing, then the service rate should also be increased so that the queue length is empty.

Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis

Motivated by the recent adoption of tactical pricing strategies in manufacturing settings, this paper studies a problem of dynamic pricing for a multiproduct make-to-order system. Specifically, for a multiclass Mn/M/1 queue with controllable arrival rates, general demand curves, and linear holding costs, we study the problem of maximizing the expected revenues minus holding costs by selecting a pair of dynamic pricing and sequencing policies. Using a deterministic and continuous (fluid model) relaxation of this problem, which can be justified asymptotically as the capacity and the potential demand grow large, we show the following: (i) greedy sequencing (i.e., the cμ-rule) is optimal, (ii) the optimal pricing and sequencing decisions decouple in finite time, after which (iii) the system evolution and thus the optimal prices depend only on the total workload. Building on (i)–(iii), we propose a one-dimensional workload relaxation to the fluid pricing problem that is simpler to analyze, and leads to intuitive and implementable pricing heuristics. Numerical results illustrate the near-optimal performance of the fluid heuristics and the benefits from dynamic pricing.

The M/M/c Interdependent Queueing Model with Controllable Arrival Rates

In this paper we consider an M/M/c interdependent queueing model with controllable arrival rates. The steady state solutions and the system characteristics are derived and analyzed for this model. The results we have obtained are merely the extension of those for M/M/1 interdependent queueing model with controllable arrival rates discussed by K. Srinivasa Rao, P.Srinivasa Rao, T.Shobha [3]. The corresponding results of usual M/M/c queueing model are deduced as a special case of this model.

The M/M/1 Interdependent Queueing Model with Controllable Arrival Rates

In this paper we introduce an M/M/1 interdependent queueing model with controllable arrival rates. These models are much useful in analysing the practical situations arising at places like, data voice transmission, computer communication systems and neuro-physiological problems. The steady state solutions of the model are derived. The system characteristics are obtained and analysed. It is observed that the mean dependence rate between the arrival and service processes can reduce the congestion in queues and delays in transmission. This model also includes the earlier models as particular cases for specific or limiting values of the parameters.