scholarly journals Approximated Transient Queue Length and Waiting Time Distributions via Steady State Analysis

2005 ◽  
Vol 21 (2-3) ◽  
pp. 725-744 ◽  
Author(s):  
B. Van Houdt ◽  
C. Blondia
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Queue Length ◽  
Steady State Analysis ◽  
Waiting Time Distributions ◽  
State Analysis

scholarly journals An analysis of steady-state distribution in M/M/1 queueing system with balking based on concept of statistical mechanics

2019 ◽  
Author(s):  
IKUO ARIZONO ◽  
Yasuhiko Takemoto
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Queue Length ◽  
Queueing System ◽  
Analysis Model ◽  
Steady State Distribution ◽  
Steady State Analysis ◽  
Extended Analysis ◽  
The Moment ◽  
State Analysis

The phenomenon of balking has been considered frequently in the steady-state analysis of the M/M/1 queueing system. Balking means the phenomenon that a customer who arrives at a queueing system leaves without joining a queue, since he/she is disgusted with the waiting queue length at the moment of his/her arrival. In the traditional studies for the steady-state analysis of the M/M/1 queueing system with balking, it has been typically assumed that the arrival rates obey an inverse proportional function for the waiting queue length. In this study, based on the concept of the statistical mechanics, we have a challenge to extend the traditional steady-state analysis model for the M/M/1 queueing system with balking. As the result, we have defined an extended analysis model for the M/M/1 queueing system under the consideration of the change in the directivity strength of balking. In addition, the procedure for estimating the strength of balking in this analysis model using the observed data in the M/M/1 queueing system has been also constructed.

scholarly journals A steady-state analysis of a hair salon as a single-queue, multi-server system to optimize the waiting time in a queue

2020 ◽  
Vol 10 (3) ◽  
pp. 22-32
Author(s):  
Sambhav Kharel ◽  
◽  
Bhandari Roshan ◽  
Satish K C ◽  
Aayush Bhattrai ◽  
...  
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Steady State Analysis ◽  
Hair Salon ◽  
Multi Server ◽  
Server System ◽  
State Analysis

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

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