Search Results (4)

Retrial queues are used extensively to model many practical problems in service systems, call centers, data centers, and computer network systems. The average waiting time is the main observable characteristic of the retrial queues. Long queues may cause negative impacts such as waste of manpower and unnecessary crowding leading to suffocation, and can even cause trouble for customers and institutions. Applying control chart technology can help managers analyze customers’ waiting times to improve the effective performance of service and attention. This paper pioneers the developing and detailed study of a waiting time control chart for a retrial queue with general service times. Two waiting time control charts, the Shewhart control chart, and a control chart using the weighted variance method are constructed in this paper. We present three cases for the Shewhart control chart in which the service time obeys special distributions, such as exponential, Erlang, and hyper-exponential distributions. The case of an exponentially distributed service time is also presented for the control chart using the weighted variance method. Based on the numerical simulations conducted herein, managers can better monitor and analyze the customers’ waiting times for their service systems and take preventive measures. Full article

In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well. Full article

The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation. Full article

A multi-server retrial queue with a hyper-exponential service time is considered in this paper. The study is performed by the method of asymptotic diffusion analysis under the condition of long delay in orbit. On the basis of the constructed diffusion process, we obtain approximations of stationary probability distributions of the number of customers in orbit and the number of busy servers. Using simulations and numerical analysis, we estimate the accuracy and applicability area of the obtained approximations. Full article