مجله بین المللی محاسبات و مدل سازی ریاضی
سال نهم شماره 1 (Winter 2019)

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customers waiting for service are subject to reneging and the reneging times are also assumed to be geometrically distributed. The explicit expressions for the steady-state probabilities are obtained recursively from the difference equations that represent the model. Closed form expressions of the system size are also derived both during regular busy period and during $WV$. In addition, we obtain some other performance measures and a cost model is formulated to determine the optimal service rate during working vacation.

In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained from Ethiopia commodity exchange (ECX) market to analyse the prices fluctuations.The natures of log-returns of the prices exhibit asymmetric heavy tails and high kurtosis. We used jump diffusion models for modeling and option pricing on commodity prices. The method of maximum likelihood is applied to estimate the parameters under the models. The root mean square error (RMSE) is used to test the goodness of fitting for the models to the data. This test indicates that the models fit the data well. The techniques of analytical and Monte Carlo simulation are used to find the call option pricing of the commodity prices. Based on the empirical results, we conclude that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of the commodity prices.

Nowadays high trend of human machinery life, high utilizing vehicles, avoiding urban public place along with neglecting identity, cultural and social values of these places make that the places in urban different scales dismiss their importance and real role. In recent decades, designing public places in urban different scales has been considered as awesome effort to meet human social needs. Therefor the purpose of writing the current research is to identify and rank driving affecting factors on designing cultural center in Tehran. The research is applicable from goal view and descriptive from data collection. Data gathering tool is questionnaire from which library and fieldwork were utilized for its designation. Statistical society includes 10000 people who pass or exist in special region of Tehran from which 384 ones were selected as statistical sample. Sampling strategy was simple random too. To measure affecting factors on designing cultural center, five main dimensions include physical, social, activities, economic and environmental factors were utilized. For this mean, a questionnaire includes 45 questions was designed and distributed among statistical society. The results of applying structural equation model in LISREL software environment illustrated that all mentioned dimensions affect significantly and positively on designing cultural center. Meanwhile the influence of environmental factors on designing cultural center was more than others. Continuously by applying fuzzy TOPSIS technique, all sub criteria were ranked that “adjoining nature and natural elements”, “existing green area in enclosure” and “facility of study” were selected as the most important factors.

In this paper, the common centralized DEA models are extended to the bi-level centralized resource allocation (CRA) models based on revenue efficiency. Based on the Karush–Kuhn–Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). A recurrent neural network is developed for solving this one-level mathematical programming problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed neural network is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, an illustrative example is elaborated to substantiate the applicability and effectiveness of the proposed approach.

An analysis of heat transfer in the flow of a viscous, in-compressible fluid along an infinite porous plate is presented when the plate is subjected to a transverse sinusoidal suction. The flow field becomes three-dimensional due to this type of suction velocity. Expressions for the flow and temperature fields are obtained by series expansion method. It is found during the course of discussion that due to more addition of viscous dissipative heat the temperature in the boundary layer increases or decreases accordingly as E> 0 or E<0.

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obtain the stationary distribution for mean queue length. Moreover, we have derived the distributions for the mean queue length and the mean waiting time and obtained their stochastic decomposition structures if N=2. Finally, numerical examples are presented.