Application of EM-Algorithm for Approximation of Correlated Traffic Probabilities Density by Hyperexponents

An accurate assessment of the quality of service parameters in modern information communication networks is a very important task. This paper proposes the use of hyperexponential distributions to solve the problem of approxi-mating an arbitrary probability density in the G/G/1 system for the case when the approximation by a system of the type H2/H2/1 is assumed. To determine the parameters of the probability density of the hyperexponential distribu-tion, it is proposed to use EM- algorithm that provides fairly simple use cases for uncorrelated flows. In this paper, we propose a variant of the EM algorithm implementation for determining the parameters of the hyperexponential distribution in the presence of correlation properties of the analyzed flow.

Mathematical Model of Call Center in the Form of Multi-Server Queueing System

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.

Stochastic approach to model spot price and value forward contracts on energy markets under uncertainty

The paper deals with a model of electricity spot prices. The proposed dynamics of electricity spot prices is driven by a mean reverting diffusion with jumps having hyperexponential distribution. The analytical formula for the forward contract’s price is derived in a crisp case. Inasmuch as the model parameters are considered to be evaluated imprecisely, their fuzzy counterparts are introduced. With usage of the fuzzy arithmetic, the analytical expression for the forward contract’s price is derived. Several numerical examples highlighting attributes of the fuzzy forward electricity prices are brought out.

Delay announcements for call centers with hyperexponential patience modeling

Purpose The purpose of this paper is to provide delay announcements for call centers with hyperexponential patience modeling. The paper aims to employ a state-dependent Markovian approximation for informing arriving customers about anticipated delay in a real call center. Design/methodology/approach Motivated by real call center data, the patience distribution is modeled by the hyperexponential distribution and is analyzed by its realistic significance, with and without delay information. Appropriate M/M/s/r+H2 queueing model is structured, including a voice response system that is employed in practice, and a state-dependent Markovian approximation is applied for computing abandonment. Based on this approximation, a method is proposed for estimating virtual delays, and it is investigated about the problem of announcing virtual delays to customers upon their arrival. Findings There are two parts of findings from the results obtained from the case study and a numerical study of simulation comparisons. First, using an H2 distribution for the abandonment distribution is driven by an empirical study which shows its good fit to real-life call center data. Second, simulation experiments indicate that the model and approximation are reasonable, and the state-dependent Markovian approximation works very well for call centers with larger pooling. It is concluded that our approach can be applied in a voice response system of real call centers. Originality/value Many results pertain to announcing delay information, customer reactions and links to estimating hyperexponential distribution based on real data that have not been established in previous studies; however, this paper analytically characterizes these performance measures for delay announcements.