Parametric Non-linear programming approach for N-policy queues with infinite capacity

This paper proposes a procedure to construct the membership function of N-policy queue with infinite capacity.  By using mathematical programming we construct the membership function of the system performance measure in which arrival rate and service rate are fuzzy numbers.  Based on a-cut approach and Zadeh’s extension principle, the fuzzy queues are converted into a family of crisp queues.  Suitable real world example is exemplified to analyze N-policy fuzzy queues.  Extending this model to fuzzy environment it would have further more wider applications

A multiple channel queueing model under an uncertain environment with multiclass arrivals for supplying demands in a cement industry

In recent years, cement consumption has increased in most Asian countries, including Malaysia. There are many factors which affect the supply of the increasing order demands in the cement industry, such as traffic congestion, logistics, weather and machine breakdowns. These factors hinder smooth and efficient supply, especially during periods of peak congestion at the main gate of the industry where queues occur as a result of inability to keep to the order deadlines. Basic elements, such as arrival and service rates, that cannot be predetermined must be considered under an uncertain environment. Solution approaches including conventional queueing techniques, scheduling models and simulations were unable to formulate the performance measures of the cement queueing system. Hence, a new procedure of fuzzy subset intervals is designed and embedded in a queuing model with the consideration of arrival and service rates. As a result, a multiple channel queueing model with multiclass arrivals, (M1, M2)/G/C/2Pr, under an uncertain environment is developed. The model is able to estimate the performance measures of arrival rates of bulk products for Class One and bag products for Class Two in the cement manufacturing queueing system. For the (M1, M2)/G/C/2Pr fuzzy queueing model, two defuzzification techniques, namely the Parametric Nonlinear Programming and Robust Ranking are used to convert fuzzy queues into crisp queues. This led to three proposed sub-models, which are sub-model 1, MCFQ-2Pr, sub-model 2, MCCQESR-2Pr and sub-model 3, MCCQ-GSR-2Pr. These models provide optimal crisp values for the performance measures. To estimate the performance of the whole system, an additional step is introduced through the TrMF-UF model utilizing a utility factor based on fuzzy subset intervals and the α-cut approach. Consequently, these models help decision-makers deal with order demands under an uncertain environment for the cement manufacturing industry and address the increasing quantities needed in future

Perceptionization of FM/FD/1 queuing model under various fuzzy numbers

We present a FM/FD/1 queuing model with unbounded limit under different fuzzy numbers. The arrival (landing) rate and service (administration) rate are thought to be fuzzy numbers such as triangular, trapezoidal and pentagonal fuzzy numbers. Because random event can only be observed in an uncertain manner, the fuzzy result of an uncertainty mapping is a fuzzy random variable. Consequently, it is conceivable to characterize the specific connection between randomness and fuzziness. The execution proportions of this lining miniature are fuzzified after that examined by utilizing α-cut estimations and DSW algorithm (Dong, Shah and Wong). Relating to different fuzzy numbers, the numerical precedents are delineated to test the attainability of this model (miniature). A comparative illustration corresponding to each fuzzy number is accomplished for various estimations of α

Analysis on Random Fuzzy Queueing Systems with Finite Capacity

This paper discusses random fuzzy queueing systems with finite capacity, where the interarrival times and service times are characterized as random fuzzy variables. Fuzzy simulation techniques are designed to estimate the membership degree, the expected value of system length, and the credibility measure that the system length does not exceed a predetermined level. Furthermore, the rough figures of the membership function and credibility distribution function of the system length can be obtained. Finally, an example is given to illustrate the effectiveness of the presented techniques

The FMX/FM/1 Queue with Multiple Working Vacation

This study investigates the batch arrival FMX/FM/1 queue with multiple working vacation. For this fuzzy queuing model, this research obtains some performance measure of interest such as mean system length, mean system sojourn time, mean busy period for the server and working vacation period. Finally, numerical results are presented to show the effects of system parameters

The analysis of M/M/1 queue with working vacation in fuzzy environment

This study investigates the FM/FM/1 queue with working vacation. For this fuzzy queuing model, the researcher obtains some performance measure of interest such as the regular busy period, working vacation period, stationary queue length and waiting time. Finally, numerical results are presented to show the effects of system parameters

Predictor Analysis of the Non-parametric Bulk Arrival Fuzzy Queueing System

In general, queueing methodology is most helpful for design the system and that may achieve the described performance level. This paper, we discuss the fuzzy queueing model with fuzzy parameter. First we construct the membership function of the fuzzy queueing character where the arrival and service rates are triangular fuzzy numbers. Consider the service node as k-phase and to provide the equal service rate in all the phases. Second we shows that the method for constructing the membership function of finite capacity queueing system. A pair of nonlinear program is developed to describe the family of crisp membership functions of finite capacity through which the membership functions of the system performance measures are derived. Finally, we obtain the lower and upper bound of the system performance measure at the different possibility level of alpha. Third we analyze the optimal level of the queueing system, this work extended in [13, 14]. A numerical example is solved successfully

On Markov Chains with Uncertain Data

In this paper, a general method is described to determine uncertainty intervals for performance measures of Markov chains given an uncertainty region for the parameters of the Markov chains. We investigate the effects of uncertainties in the transition probabilities on the limiting distributions, on the state probabilities after n steps, on mean sojourn times in transient states, and on absorption probabilities for absorbing states. We show that the uncertainty effects can be calculated by solving linear programming problems in the case of interval uncertainty for the transition probabilities, and by second order cone optimization in the case of ellipsoidal uncertainty. Many examples are given, especially Markovian queueing examples, to illustrate the theory.Markov chain;Interval uncertainty;Ellipsoidal uncertainty;Linear Programming;Second Order Cone Optimization