scholarly journals Analysis of Flexible Batch Service Queueing System to Constrict Waiting Time of Customers

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Deena Merit C. K. ◽  
Haridass M
Keyword(s):  
Arrival Time ◽  
Queueing System ◽  
Clinical Laboratory ◽  
Waiting Times ◽  
Distribution Center ◽  
Expiration Date ◽  
Suggested Model ◽  
Numerical Illustration ◽  
Bulk Service ◽  
Number Of Customers

When the required number of customers is available in the general bulk service (GBS) queueing system, the server begins service. Otherwise, the server will remain inactive until the number of consumers in the queue reaches that minimum required number. Customers that have already come must wait throughout this time, regardless of their arrival time. In some circumstances, like specimens awaiting testing in a clinical laboratory or perishable commodities awaiting delivery, it is necessary to finish services before the expiration date. It might only be achievable if consumers’ waiting times are kept under control. As a result, the flexible general bulk service (FGBS) rule is developed in this article to provide flexibility in batching. The effectiveness of FGBS implementation has been demonstrated using two examples: a clinical laboratory and a distribution center. To justify the suggested model, a simulation study and numerical illustration are provided.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (4) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (04) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

Time-dependent solution and optimal control of a bulk service queue

1997 ◽  
Vol 34 (01) ◽  
pp. 258-266
Author(s):  
Shokri Z. Selim
Keyword(s):  
Queueing System ◽  
Maximum Size ◽  
Time Dependent ◽  
Optimal Service ◽  
Bulk Service ◽  
Service Rates ◽  
Finite Time Horizon ◽  
Number Of Customers ◽  
Time Dependent Solution ◽  
Dependent Probability

We consider the queueing system denoted by M/MN /1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon.

Analysis of a non-preemptive priority multiserver queue

1988 ◽  
Vol 20 (04) ◽  
pp. 852-879 ◽  
Author(s):  
H. R. Gail ◽  
S. L. Hantler ◽  
B. A. Taylor
Keyword(s):  
Probability Distribution ◽  
Queueing System ◽  
Waiting Times ◽  
Complex Variables ◽  
Arrival Process ◽  
Preemptive Priority ◽  
Multiple Servers ◽  
The Mean ◽  
Equilibrium Probability ◽  
Number Of Customers

We consider a non-preemptive priority head of the line queueing system with multiple servers and two classes of customers. The arrival process for each class is Poisson, and the service times are exponentially distributed with different means. A Markovian state description consists of the number of customers of each class in service and in the queue. We solve a matrix equation to obtain the generating function of the equilibrium probability distribution by analyzing singularities of the equation coefficients, which are meromorphic matrices of two complex variables. We then obtain the mean waiting times for each class.

scholarly journals Some results for the general bulk service queueing system

1981 ◽  
Vol 23 (2) ◽  
pp. 161-179 ◽  
Author(s):  
D.F. Holman ◽  
M.L. Chaudhry ◽  
A. Ghosal
Keyword(s):  
Generating Functions ◽  
Queueing System ◽  
Expected Value ◽  
Queue Size ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Distribution Probability ◽  
Poisson Stream ◽  
Bulk Service ◽  
Number Of Customers

This paper deals with a general bulk service queueing system with one server, for which customers arrive in a Poisson stream and the service is in bulk. The maximum number of customers to be served in one lot is B (capacity), but the server does not start service until A (quorum, less than B) customers have accumulated; and the service time follows a general probability distribution. Probability generating functions of the distributions Pn and , under equilibrium, have been derived by using the supplementary variable technique. An expression has been derived for the expected value of the queue size and its relation with the expected value of the waiting time of a customer has been explored. A numerical case has been worked out on the assumption that bulk service follows a specified Erlangian distribution.

Modelling and simulation analysis of a bulk queueing system

Kybernetes ◽  
2019 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nithya R.P. ◽  
Haridass M.
Keyword(s):  
Simulation Model ◽  
Textile Industry ◽  
Performance Metrics ◽  
Queueing System ◽  
Simulation Analysis ◽  
Simulation Modelling ◽  
Industrial Applications ◽  
Numerical Illustration ◽  
Content Type ◽  
Bulk Service

Purpose The purpose of this paper is to provide simulation modelling for bulk arrival bulk service queueing system involved in a textile industry and analyze the performance metrics. Design/methodology/approach This paper describes the simulation modelling of a bulk queueing system with limited number of admissions and multiple vacations. The model is developed for the proposed queueing system using Flexsim 2017, and it is explained through an application observed in a textile industry involving the process of cone winding. Findings In this paper, the simulation model has been developed to study the behaviour of queues at different resources in a production system. Various performance measures such as average components, average waiting time, total number of inputs and outputs, processing time and idle time involved in a textile industry are evaluated using simulation and justified through numerical illustration. Practical implications The proposed simulation model may be used in various scenarios wherever a real time situation exists related to bulk queueing system. The results produced in this paper can be used by the manufacturing industries to enhance the need-based accuracy. It is worth pointing out that the findings are of direct practical relevance and can be successfully used for a number of industrial applications. Originality/value The approach suggested in this paper attempts to deal with the queueing system involved in a textile industry and provides numerical results in less time with less computer resources. It provides a reasonably good approximation for simple and complex queueing models where it is difficult to find closed form of theoretical results.

Analysis of a non-preemptive priority multiserver queue

1988 ◽  
Vol 20 (4) ◽  
pp. 852-879 ◽  
Author(s):  
H. R. Gail ◽  
S. L. Hantler ◽  
B. A. Taylor
Keyword(s):  
Probability Distribution ◽  
Queueing System ◽  
Waiting Times ◽  
Complex Variables ◽  
Arrival Process ◽  
Preemptive Priority ◽  
Multiple Servers ◽  
The Mean ◽  
Equilibrium Probability ◽  
Number Of Customers

We consider a non-preemptive priority head of the line queueing system with multiple servers and two classes of customers. The arrival process for each class is Poisson, and the service times are exponentially distributed with different means. A Markovian state description consists of the number of customers of each class in service and in the queue. We solve a matrix equation to obtain the generating function of the equilibrium probability distribution by analyzing singularities of the equation coefficients, which are meromorphic matrices of two complex variables. We then obtain the mean waiting times for each class.

Time-dependent solution and optimal control of a bulk service queue

1997 ◽  
Vol 34 (1) ◽  
pp. 258-266 ◽  
Author(s):  
Shokri Z. Selim
Keyword(s):  
Queueing System ◽  
Maximum Size ◽  
Time Dependent ◽  
Optimal Service ◽  
Bulk Service ◽  
Service Rates ◽  
Finite Time Horizon ◽  
Number Of Customers ◽  
Time Dependent Solution ◽  
Dependent Probability

We consider the queueing system denoted by M/MN/1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon.

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (01) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

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