Optimisation of single-queue service delivery systems using a Markovian approach (original) (raw)
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International Journal of Science and Research (IJSR)
The ultimate objective of the analysis of queuing systems is to understand the behaviour of their underlying process so that informed and intelligent decisions can be made by the management. The application of queuing concepts is an attempt to minimize cost through minimization of inefficiency and delays in a system. Various methods of solving queuing problems have been proposed. In this study we have explored single –server Markovian queuing model with both interarrival and service times following exponential distribution with parameters and , respectively, and unlimited queue size with FIFO queuing discipline and unlimited customer population. We apply this model to catering data and estimate parameters for the same. A sensitivity analysis is the carried out to evaluate stability of the system.
African Journal of Physical Sciences, 2012
This study assumed that the inter-arrival and service times are memoryless; thus the probability of customers (n = 0, 1, 2, …) being in the queue was derived. Other parameters, like the average number of customers in the queue and the average time a customer spends on the queue were derived. Distribution of the sojourn, waiting, and service times were subsequently derived, using Laplace-Stieltjes transform. These were achieved by considering the time-dependent behavior of the Markovian queueing model, that is, the number of customers in the system at a time with the help of a flow transition diagram used for a transition from state n to state (n+1) (an arrival), and for the transition from state (n+1) to state n, and since the exponential distribution is memoryless. we do not have to remember the time the last customer arrives, and the service times are not of interest, and this information does not yield a better prediction of the future. A direct approach using a second-order recurrence relation with constant coefficient, limiting behavior, recursion process, and the generating function of a number of customers in the system with the application of the balance principle PASTA property and Little's law was used to arrive at the aforementioned parameters. A numerical example based on the application of the model parameter was given using Grace and Gloria Supermarket Agbowo, Ibadan to test our derived parameter
Bulk Service Queuing System with Impatient Customers: A Computational Approach
Thailand Statistician, 2017
The paper investigates a M / M ( b , b ) /1 queuing model with bulk service. The server serves the customers in batches of fixed size b , and the service time is assumed to be exponentially distribution. Customers arrive to the system as a Poisson process and may renege after waiting in the queue for an exponentially distributed time. The reneging of a customer depends on the state of the system. The model is analyzed to find the different measures of effectiveness of the model. The approach adopted is based on embedded Markov chains.
Bulk Service Queuing System A Computational Approach
2016
The paper investigates a M/M/1 queuing model with bulk service customers in batches of fixed size b, and the service time is assumed to be exponentially distribution. Customers arrive to the system as a Poisson process and may renege after waiting in the queue for an exponentially distributed time the system. The model is analyzed to find the different measures of effectiveness of the model approach adopted is based on embedded Markov chains ______________________________
The-Application-of-Queuing-Analysis-in-modeling-Optimal-Service-level.pdf
Queues are common scenario faced in the modern day Banks and other financial Institutions. Queuing theory is the mathematical study of waiting lines; this can also be applicable queues in the banking system. This study examine the queuing system at Guarantee Trust Bank (GTB), putting into consideration the waiting time spend by Customers, Service time spend by a Customer and the average cost a customer loses while in queue and the service cost of each server in order to optimize the system. The First Come First Serve (FCFS) Multi-Server queuing model was used to model the queuing process. The waiting time was assumed to follow a Poisson distribution while the service rate follows an Exponential distribution. This study adopted a case study approach by randomly administering questionnaires, interviews and observation of the participants. The data were collected at the GTB cash deposit unit for four days period. The data collected were analyzed using TORA optimization window based software as well as standard queuing formula. The results of the analysis showed that the average queue length, waiting time of customer with a minimum Total Cost that utilize the system is by using five Servers against the present server level of Three Servers which incur a high total cost to both the Customers and the system.
The “Sensitive” Markovian queueing system and its application for a call center problem
Annals of Operations Research, 2018
In this paper, we study the M n /M n /c/K + M n queueing system where customers arrive according to a Poisson process with state-dependent rates. Moreover, the rates of the exponential service times and times to abandonment of the queued customers can also change whenever the system size changes. This implies that a customer may experience different service rates throughout the time she is being served. Similarly, a queued customer can change her patience time limits while waiting in the queue. Thus, we refer to the analyzed system as the "sensitive" Markovian queue. We conduct an exact analysis of this system and obtain its steady-state performance measures. The steady-state system size distribution yields itself via a birth-death process. The times spent in the queue by an arbitrary or an eventually served customer are represented as the times until absorption in two continuous-time Markov chains and follow Phase-type distributions with which the queueing time distributions and moments are obtained. Then, we demonstrate how the M n /M n /c/K + M n queue can be employed to approximately yet accurately estimate the performance measures of the M n /GI/c/K + GI type call center.
Research Square (Research Square), 2022
A system with two heterogeneous servers with impatient customers and finite capacity is considered. The admission control of customers is based on F-policy. This paper is based on M/M/2 queues, and presents the study of two heterogeneous servers where one server is the primary server and other is secondary. Customers are primarily served by the main server, who also takes customer's feedback into account. If customers are unsatisfied and opt for further service, the second server will serve them. The main server considered is unreliable, that is, it may breakdown at any time. The main server will go for vacation whenever there is no customer to serve. To analyze the performance of the model, we calculated the measures of performance and did the cost analysis. Impact of F-policy on system's estimated profit is shown. At last, conclusions are drawn.
On Application of Queuing Models to Customers Management in Banking System
Queue is a common sight in banks these days especially on Mondays and on Fridays. Hence queuing theory which is the mathematical study of waiting lines or queue is suitable to be applied in the banking sector since it is associated with queue and waiting line where customers who cannot be served immediately have to queue(wait) for service. The aim of this paper is to determine the average time customers spend on queue and the actual time of service delivery, thereby examining the impact of time wasting and cost associated with it.We used the Markovian birth and death process to analyze the queuing model , which is the Multiple servers, single queue, (M/M/S) queuing model to analyze the data collected by observation from a bank and from the results obtained, the arrival rate is 0.1207 and the service rate is 0.156, the probability that the servers are idle is 0.44 which shows that the servers will be 44% idle and 56% busy, the expected number in the waiting line is 0.1361, the expected number in the system is 0.9098. The expected waiting time in the queue is 1.276 and the expected total time lost waiting in one day is 3.2664 hours, the average cost per day for waiting is ₦65.328 and from the calculation of the comparing solutions, the average cost per day from waiting is ₦7.966 which means that there had been a saving in the expected cost of ₦65.328-₦7.966 = ₦57.362. This means that with three servers, the average cost from waiting is reduced. Hence we concluded that the aim and objectives of this paper was achieved.