Unequal Service Rates Research Articles

Comparison of Non-Preemptive Priority Queuing Performance Using Fuzzy Queuing Model and Intuitionistic Fuzzy Queuing Model with Different Service Rates

This study provides non-preemptive priority fuzzy and intuitionistic fuzzy queuing models with unequal service rates. For performance evaluations of the industrial, supply chain, stock management, workstations, data exchange, and telecommunications equipment, non-preemptive priority queues are appropriate. The parameters of non-preemptive priority queues may be fuzzy due to unpredictable causes. The primary goal of this research is to compare the performance of a non-preemptive queuing model applying fuzzy queuing theory and intuitionistic fuzzy queuing theory. The performance metrics in the fuzzy queuing theory model are given as a range of values, however, the intuitionistic fuzzy queuing theory model offers a multitude of values. Both the arrival rate and the service rate are triangular and intuitionistic triangular fuzzy numbers in this case. An analysis is provided to identify the quality metrics by using a developed methodology through which without converting into crisp values we are taking the fuzzy values as it is and to demonstrate the viability of the suggested method, two numerical problems are solved.

Analysis of Fuzzy Non-preemptive Priority Queuing Model with Unequal Service Rate

This article provides an effective method to analyze the performance measures of non-preemptive fuzzy priority queues with unequal service rates. Here the arrival rate and the service rate are in fuzzy numbers. Using a new ranking method, the fuzzy values are reduced to the crisp values. For that cause, both the Triangular Fuzzy Number (TFN) and Trapezoidal Fuzzy Number (TpFN) are chosen to establish the proposal's effectiveness. An illustration is given to find the efficiency of the performance measures of the fuzzy queuing model.

Analysis of Fuzzy Priority Queue with Two Classes of Customers and Unequal Service Rates using Mixed Integer Non Linear Programming Approach

Analysis of Fuzzy Priority Queue with Two Classes of Customers and Unequal Service Rates using Mixed Integer Non Linear Programming Approach

A single server retrial fuzzy queue with priority and unequal service rates

A single server retrial fuzzy queue with priority and unequal service rates

A single server fuzzy queues with priority and unequal service rates

This article presents to develop a new mathematical model to construct membership functions of the fuzzy single channel queueing model F(M1, M2)/F(M1, M2)/1/PR-NP with two class of non-preemptive priority with unequal service rates. The main idea of this article is to merge between mathematical programming technique and Yager's ranking method by using α-cut approach and Zadeh extension principle to transform fuzzy queues into a family of conventional crisp (distinct) queues in this context. A numerical example is given to explain the validity of this new approach to obtain real exact values under different levels of α in the system.

A single server fuzzy queues with priority and unequal service rates

This article presents to develop a new mathematical model to construct membership functions of the fuzzy single channel queueing model F(M1, M2)/F(M1, M2)/1/PR-NP with two class of non-preemptive priority with unequal service rates. The main idea of this article is to merge between mathematical programming technique and Yager's ranking method by using α-cut approach and Zadeh extension principle to transform fuzzy queues into a family of conventional crisp (distinct) queues in this context. A numerical example is given to explain the validity of this new approach to obtain real exact values under different levels of α in the system.

The Tail Behavior of a Longest-Queue-Served-First Queueing System: A Random Walk in the Half Plane

In this article, we consider the longest-queue-served-first queueing system, in which two types of customers arrive, independently and respectively according to two Poisson processes with possibly unequal arrival rates, to two separate queues served, with possibly unequal service rates, by a single exponential server. This system finds important applications and has been studied before. Our focus is on the tail asymptotic behavior for the stationary distribution when the system is stable. We model this system into a reflected random walk in the half plane. This random walk reveals two different properties, respectively, along the direction of the minimum of the two queues and the direction of the difference between the two queues. Specifically, the one-dimensional process for the minimum is reducible, which makes the tail analysis along the difference direction easier, but the process for the difference is irreducible, for which the analysis is more challenging (similar to the analysis for a non-singular genus one reflected random walk). We extend the kernel method for random walks in the quarter plane to this system to obtain exact tail asymptotic expressions along both directions, which are new contributions to the literature.

Polling Models with Unequal Service Rates under Limited Service Policies—Sharp Asymptotics

We derive asymptotic expressions for the distribution of the total queue length in a polling model with two classes of customers and unequal service rates. The server employs a scheduling policy that alternately visits each queue, with the maximum number served in each visit potentially being different for each queue. We provide sufficient conditions for the behaviour to lie in one of two regimes, depending on the system parameters. The first regime, called codominant, has both queues tending to grow as the total system size grows. The single-class dominant regime has only one queue tending to grow as the total system size grows. Finally, we present numerical results that demonstrate that the developed conditions are only sufficient and comment on the implications of this observation.

Rare events in series of queues

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

Rare events in series of queues

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

The Power-Series Algorithm Applied to the Shortest-Queue Model

An iterative numerical technique for the evaluation of queue length distribution is applied to multiserver systems with queues in parallel in which customers join (one of) the shortest queues upon arrival. The technique is based on power-series expansions of the state probabilities as functions of the load of the system. The convergence of the series is accelerated by applying a modified form of the epsilon algorithm. The shortest-queue model lends itself particularly well to a numerical analysis by means of the power-series algorithm due to a specific property of this model. Numerical values for the mean and the standard deviation of the total number of customers and the waiting times in stationary symmetrical systems are obtained for practically all values of the load for systems with up to ten queues and for a load not exceeding 75% for systems with up to 30 queues. Data are also presented for systems with four queues and unequal service rates.

Limited space double channel markovian queue with heterogeneous servers

For a double channel Markovian queue with finite waiting space and unequal service rates at the two counters, the difference equations satisfied by the Laplace transforms of the state probabilities at finite time are solved and the state probabilities have been obtained. The closed form of the state probabilities can be used to obtain the important parameters of the system.