Balking Rate Research Articles

The Evaluation of M/M/2 Queuing Framework with Two Heterogeneous Servers for Balking and Reneged Customers

Queuing hypothesis is a quantitative method which comprises in building scientific models of different sorts of lining frameworks. Occupied time of the framework is broke down and mean holding up time in the stationary system processed. At long last, some numerical outcomes are introduced to demonstrate the impact of model parameters on the framework execution measures. The traveling server, nonetheless, comes back to landing which is used to offer at a low rate whereas the other server is occupied. At whatever point the framework ends up and the subsequent server leaves for a working excursion while the principal server stays inert in the framework. These models can be utilized for making expectations about how the framework can change with requests. The framework is examined in the enduring state utilizing lattice geometric strategy. The clients enter the line in the Poisson manner and the time of each bunch size is dared to be circulated exponentially as for mean ward clump size and clients may balk away or renege when the holding up the line of the clients, in general, be exceptionally enormous. This work exhibits the investigation of a recharging input different working excursions line with balking, reneging and heterogeneous servers. Queuing hypothesis manages the investigation of lines and lining conduct. Different execution proportions of the model, for example, anticipated framework length, anticipated balking rate and reneging rate have been talked about. The technique breaks down an M/M/2 lining framework with two heterogeneous servers, one of which is constantly accessible however the different travels without clients sitting tight for service. During a working vacation period, the subsequent server gives administration at a slower rate as opposed to totally ceasing service. The relentless state probabilities of the model are advantageous and recursive strategies.

Algorithmic computation of steady-state probabilities in an almost observable GI/M/c queue with or without vacations under state dependent balking and reneging

We consider an almost observable GI/M/c/N queue with customer impatience with or without multiple synchronous vacations under state-dependent balking. Upon arriving, a customer joins or refuses to join the system based on certain state dependent joining/balking probabilities. Once an arriving customer joins the system and finds all the servers busy, it initiates an exponentially distributed impatience timer with random duration T. An equilibrium balking strategy is discussed for constant balking as a special case of state-dependent balking. In the constant balking case, the waiting time of a customer in a queueing system has been associated with a linear cost-reward structure for estimating the net benefit if a customer chooses to participate in the system. A steady-state system of equations is obtained using the supplementary variable technique. After that, a recursive algorithm is proposed to obtain the stationary system-length distribution at pre-arrival and arbitrary epochs using those steady-state equations, from which the mean system sojourn time, the average reneging rate and the average balking rate are derived. Finally, we produce numerical results relating to system performance and its net benefit when investigated for different model parameters. The proposed model has applications in the modeling of balking and impatient behavior of incoming calls in a call center, multi-core computing, multi-path routing in delay sensitive communications networks.

Analysis of Power Saving Class II Traffic in IEEE 802.16E with Multiple Sleep State and Balking

Abstract The battery life of Mobile Stations in IEEE 802.16e can be extended substantially by applying the sleep mode mechanism. This paper studies an effcient method to analyze the performance of the power saving class type II for delay sensitive traffc in multiple sleep state. The incoming data frames may join or balk the buffer due to impatience with some probability. We present an M/M/1/N queueing model with balking and multiple vacations in order to exhibit the self-similar property of IEEE 802.16e. We develop a cost function to determine the optimal service rate that minimizes the total expected cost. Various performance indices such as the average number of data frames in the system, the mean waiting time of the data frame in the system, the the average balking rate due to impatience, etc. have been presented. Numerical results are provided to show the inuence of various parameters on the behavior of the system. The proposed model provides a tradeoff between the average abandon rate and the power consumption.

Balking and Reneging Multiple Working Vacations Queue with Heterogeneous Servers

This paper presents the analysis of a renewal input multiple working vacations queue with balking, reneging and heterogeneous servers. Whenever the system becomes empty the second server leaves for a working vacation whereas the first server remains idle in the system. During a working vacation the second server provides service at a slower rate rather than completely stopping service. The steady-state probabilities of the model are obtained using supplementary variable and recursive techniques. Various performance measures of the model such as expected system length, expected balking rate, etc., have been discussed. Finally, some numerical results have been presented to show the effect of model parameters on the system performance measures.

The warm-standby M/M/R machine repair problem with balking, reneging and service pressure coefficient

This paper studies the warm-standby M/M/R machine repair problem with balking and reneging plus service pressure coefficient. Failed machines balk (do not enter) with a constant probability (1 – b) and renege (leave the queue after entering) according to a negative exponential distribution. We use the birth-and-death results to derive the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is constructed to determine the joint optimal values of the number of repairmen, the number of warm standbys, and the joint optimal values of the service rate and the balking rate simultaneously by using twostage optimisation method. Numerical results are provided to illustrate the effectiveness of the two-stage optimisation algorithm. Sensitivity analysis is also investigated.

Cost Optimization and Sensitivity Analysis of the Machine Repair Problem with Variable Servers and Balking

We consider a machine repair model with M identical machines and variable servers considering balking concept. A recursive method is applied o develop analytical steady-state solutions. We also calculate various system performance measures, such as the expected number of failed machines, the expected number of operating machines, the expected number of busy and idle servers, average balking rate, machine availability, operative utilization, and so on. A cost model is constructed to determine the optimal values of the number of busy servers, and maintain the balking rate at a certain level. Numerical results are provided in which various system performance measures are evaluated under optimal operating conditions. Sensitivity analysis is performed to investigate the effect of changes in the system parameters on the expected cost function. Finally, numerical results are also given for illustrative purposes.

Quality of service evaluations of multicast streaming protocols

Recently proposed scalable on-demand streaming protocols have previously been evaluated using a system cost measure termed the "required server bandwidth". For the scalable protocols that provide immediate service to each client when the server is not overloaded, this paper develops simple analytic models to evaluate two client-oriented quality of service metrics, namely (1) the mean client waiting time in systems where clients are willing to wait if a (well-provisioned) server is temporarily overloaded, and (2) the fraction of clients who balk (i.e., leave without receiving their requested media content) in systems where the clients will tolerate no or only very low service delays during a temporary overload. The models include novel approximate MVA techniques that appear to extend the range of applicability of customized AMVA to include questions focussed on state probabilities rather than on mean values, and to systems in which the operating points of interest do not include substantial client queues. For example, the new AMVA models accurately estimate the server bandwidth needed to achieve a balking rate as low as one in ten thousand. The analytic models can easily be applied to determine the server bandwidth needed for a given number of media files, anticipated total client request rate and file access frequencies, and target balking rate or mean wait. Results show that (a) scalable media servers that are configured with the "required server bandwidth" defined in previous work have low mean wait but may have unacceptably high client balking rates (i.e., greater than one in twenty), (b) for high to moderate client load, only a 10 - 50% increase in the previously defined required server bandwidth is needed to achieve a very low balking rate (e.g., one in ten thousand), and (c) media server performance (either mean wait or balking rate) degrades rapidly if the actual client load is more than 10% greater than the anticipated load.

Simulation and Queueing Theory Applied to a Single-Server Queue with Advertising and Balking

We use a single-server queueing model, with limited waiting room capacity, to model a situation where the manager of a facility tries to maximize the profit generated by the facility. He advertises to attract customers. The effectiveness of advertising may depend on the reputation of the facility, which is measured by the fraction of customers who balk. We assume Poisson arrivals and allow Erlang service times to study how the variance of service times affects the optimal policy, both when the efficiency of advertising is exogenous, and when it is a function of the balking rate. We conclude that the optimal policies are similar for deterministic service times, but diverge as the variance of the service time increases.

Right turn on red- a traffic management simulation

This paper outlines a stochastic model of the right- turn-on-red (RTOR) policy for a high-density urban area consisting of one-way streets. This model is used to investigate the effects of (1) cross-street traffic volume, (2) right-turn lane traffic volume, (3) pedestrian arrival rate, and (4) balking rate for right-turning vehicles. The model provides the methodology for studying the RTOR maneuver under various conditions. Specific recommendations on when to use RTOR are developed for typical urban conditions.