Comment on “Bulk Queue Model for Computer System Analysis” [Letter to the Editor]

1975 ◽  
Vol 19 (4) ◽  
pp. 424-424
Author(s):  
E. W. Stacy
Keyword(s):  
Computer System ◽  
System Analysis ◽  
Letter To The Editor ◽  
Bulk Queue ◽  
Queue Model

Stability and heavy traffic results for the general bulk queue

1978 ◽  
Vol 10 (1) ◽  
pp. 213-231 ◽  
Author(s):  
John Dagsvik
Keyword(s):  
Initial Conditions ◽  
Heavy Traffic ◽  
Mixing Processes ◽  
Absolute Value ◽  
Bulk Queue ◽  
Unstable Case ◽  
Queue Model ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit ◽  
Gaussian Variable

In this paper we prove that the limiting distribution of the general bulk queue exists and is independent of the initial conditions if and only if the traffic intensity is less than one. We further generalize the following heavy traffic results of the GI/G/1 model to the general bulk queue model. When ρ > 1 or ρ = 1 the waiting time is distributed approximately as a Gaussian variable and the absolute value of a Gaussian variable, respectively. The exponential approximation is derived from the Wiener–Hopf matrix equations established in a previous paper while the unstable case ρ ≧ 1 is treated by means of functional central limit theorems for mixing processes.

scholarly journals ANALISIS SISTEM ANTRIAN DALAM OPTIMALISASI LAYANAN DI SUPERMARKET HYPERSTORE

2020 ◽  
Vol 12 (2) ◽  
pp. 225-237
Author(s):  
Benediktus L V Bataona ◽  
Antonio E L Nyoko ◽  
Ni Putu Nursiani
Keyword(s):  
Single Phase ◽  
System Analysis ◽  
Service Level ◽  
Optimal Number ◽  
Queuing Model ◽  
Multiple Line ◽  
First Come First Serve ◽  
Queue Model ◽  
Queue Theory ◽  
Service Optimization

The purpose of this study is to determine the average customer arrival level and average service level at the Hyperstore Supermarket and analyze the queuing system by optimizing the number of cashiers that must be set at the Hyperstore Supermarket. The results showed that the queuing model used at the Hyperstore Supermarket is Multi Channel Single Phase by applying the First Come First Serve (FCFS) queuing discipline. The average service level at the Hyperstore Supermarket is 146 people/hour. The current number of lines opened at the Hyperstore Supermarket is 6 cashiers. However, 6 cashier lines are excess even though 3 cashier lines are sufficient. Queue system analysis shows that the optimal number of cashier lines which is 1 cashier line open at 3:00 pm to 4:00, 2 cashier lines open at 16:00 to 19:00 and 3 cashiers lines opened at 19:00 to 20:00 Keywords: Queue Theory, Multiple Line Queue Model, Cashier, Service Optimization

Stability and heavy traffic results for the general bulk queue

1978 ◽  
Vol 10 (01) ◽  
pp. 213-231
Author(s):  
John Dagsvik
Keyword(s):  
Initial Conditions ◽  
Heavy Traffic ◽  
Mixing Processes ◽  
Absolute Value ◽  
Bulk Queue ◽  
Unstable Case ◽  
Queue Model ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit ◽  
Gaussian Variable

In this paper we prove that the limiting distribution of the general bulk queue exists and is independent of the initial conditions if and only if the traffic intensity is less than one. We further generalize the following heavy traffic results of the GI/G/1 model to the general bulk queue model. When ρ > 1 or ρ = 1 the waiting time is distributed approximately as a Gaussian variable and the absolute value of a Gaussian variable, respectively. The exponential approximation is derived from the Wiener–Hopf matrix equations established in a previous paper while the unstable case ρ ≧ 1 is treated by means of functional central limit theorems for mixing processes.

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