On the mean waiting time of a population constrained open tandem queueing network with constant service times

1998 ◽  
Vol 30 (10) ◽  
pp. 973-979 ◽  
Author(s):  
YOUNG RHEE ◽  
HARRY G. PERROS
Keyword(s):  
Waiting Time ◽  
Queueing Network ◽  
Mean Waiting Time ◽  
The Mean ◽  
Service Times ◽  
Constant Service Times

scholarly journals Assessment of patients waiting and service times in the ophthalmology clinic of a public tertiary hospital in Nigeria

2020 ◽  
Vol 54 (4) ◽  
pp. 231-237
Author(s):  
Lateefat B. Olokoba ◽  
Kabir A. Durowade ◽  
Feyi G. Adepoju ◽  
Abdulfatai B. Olokoba
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Sampling Technique ◽  
Tertiary Hospital ◽  
Cross Sectional Study ◽  
Ethical Review ◽  
Cross Sectional ◽  
Arrival Times ◽  
The Mean ◽  
Service Times

Introduction: Long waiting time in the out-patient clinic is a major cause of dissatisfaction in Eye care services. This study aimed to assess patients’ waiting and service times in the out-patient Ophthalmology clinic of UITH. Methods: This was a descriptive cross-sectional study conducted in March and April 2019. A multi-staged sampling technique was used. A timing chart was used to record the time in and out of each service station. An experience based exit survey form was used to assess patients’ experience at the clinic. The frequency and mean of variables were generated. Student t-test and Pearson’s correlation were used to establish the association and relationship between the total clinic, service, waiting, and clinic arrival times. Ethical approval was granted by the Ethical Review Board of the UITH. Result: Two hundred and twenty-six patients were sampled. The mean total waiting time was 180.3± 84.3 minutes, while the mean total service time was 63.3±52.0 minutes. Patient’s average total clinic time was 243.7±93.6 minutes. Patients’ total clinic time was determined by the patients’ clinic status and clinic arrival time. Majority of the patients (46.5%) described the time spent in the clinic as long but more than half (53.0%) expressed satisfaction at the total time spent at the clinic. Conclusion: Patients’ clinic and waiting times were long, however, patients expressed satisfaction with the clinic times.

Study of Industrial Model for Five-Input, Five-Stage Queueing Network

2016 ◽  
pp. 300-339
Author(s):  
Jitendra Kumar ◽  
Vikas Shinde
Keyword(s):  
Response Time ◽  
Textile Industry ◽  
Optimal Path ◽  
Queueing Network ◽  
Numerical Illustration ◽  
Mean Response Time ◽  
Final Destination ◽  
Optimal Capacity ◽  
Mean Waiting Time ◽  
The Mean

In this paper, we have developed an industrial model for textile industry with five-input, five-stage queueing network, wherein system receives orders from clients that are waiting to be served. The aim of this paper is to compute the optimal path that will provide the least response time for delivery of items to the final destination, through the five stages under queueing network. The mean number of items that can be delivered is minimum response time constitute the optimal capacity of the network. The last node in each stage of the network can be executed in the least possible response time. Various performance indices were carried out such as mean number of item in the system, mean number of item in queue, mean response time, mean waiting time. We have established the equivalent queueing network to analyze the various performance measures with numerical illustration and graph.

Realization probability in closed Jackson queueing networks and its application

1987 ◽  
Vol 19 (03) ◽  
pp. 708-738 ◽  
Author(s):  
X. R. Cao
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Queueing Networks ◽  
Sample Path ◽  
Queueing Network ◽  
Jackson Network ◽  
The Mean ◽  
Service Times ◽  
A New Technique ◽  
Number Of Customers

Perturbation analysis is a new technique which yields the sensitivities of system performance measures with respect to parameters based on one sample path of a system. This paper provides some theoretical analysis for this method. A new notion, the realization probability of a perturbation in a closed queueing network, is studied. The elasticity of the expected throughput in a closed Jackson network with respect to the mean service times can be expressed in terms of the steady-state probabilities and realization probabilities in a very simple way. The elasticity of the throughput with respect to the mean service times when the service distributions are perturbed to non-exponential distributions can also be obtained using these realization probabilities. It is proved that the sample elasticity of the throughput obtained by perturbation analysis converges to the elasticity of the expected throughput in steady-state both in mean and with probability 1 as the number of customers served goes to This justifies the existing algorithms based on perturbation analysis which efficiently provide the estimates of elasticities in practice.

scholarly journals Estimation of the mean waiting time of a customer subject to balking: a simulation study

2007 ◽  
Vol 19 (1) ◽  
pp. 63-63
Author(s):  
Jaejin Jang ◽  
Jaewoo Chung ◽  
Jungdae Suh ◽  
Jongtae Rhee
Keyword(s):  
Waiting Time ◽  
Simulation Study ◽  
Mean Waiting Time ◽  
The Mean

scholarly journals Waiting Time Problems for Patterns in a Sequence of Multi-State Trials

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1893
Author(s):  
Bara Kim ◽  
Jeongsim Kim ◽  
Jerim Kim
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Probability Generating Function ◽  
Finite Collection ◽  
Numerical Inversion ◽  
Analytic Method ◽  
Waiting Time Distribution ◽  
Mean Waiting Time ◽  
The Matrix ◽  
The Mean

In this paper, we investigate waiting time problems for a finite collection of patterns in a sequence of independent multi-state trials. By constructing a finite GI/M/1-type Markov chain with a disaster and then using the matrix analytic method, we can obtain the probability generating function of the waiting time. From this, we can obtain the stopping probabilities and the mean waiting time, but it also enables us to compute the waiting time distribution by a numerical inversion.

scholarly journals Processor-sharing and random-service queues with semi-Markovian arrivals

2005 ◽  
Vol 42 (02) ◽  
pp. 478-490
Author(s):  
De-An Wu ◽  
Hideaki Takagi
Keyword(s):  
Waiting Time ◽  
Sojourn Time ◽  
Time Distribution ◽  
Arrival Process ◽  
Interarrival Time ◽  
Size Distributions ◽  
Processor Sharing ◽  
Queue Size ◽  
Mean Waiting Time ◽  
The Mean

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-lcustomer who, upon his arrival, meetskcustomers already present in the SMP/M/1/PS queue is identical to the waiting time distribution of a type-lcustomer who, upon his arrival, meetsk+1 customers already present in the SMP/M/1/RS queue. Two sets of system equations, one for the joint transform of the sojourn time and queue size distributions in the SMP/M/1/PS queue, and the other for the joint transform of the waiting time and queue size distributions in the SMP/M/1/RS queue, are derived. Using these equations, the mean sojourn time in the SMP/M/1/PS queue and the mean waiting time in the SMP/M/1/RS queue are obtained. We also consider a special case of the SMP in which the interarrival time distribution is determined only by the type of the customer who has most recently arrived. Numerical examples are also presented.

scholarly journals The mean waiting time to a repetition

1983 ◽  
Vol 15 (01) ◽  
pp. 216-218
Author(s):  
Gunnar Blom
Keyword(s):  
Waiting Time ◽  
Mild Condition ◽  
Random Variables ◽  
Stationary Sequence ◽  
Mean Waiting Time ◽  
The Mean

Let X 1, X2, · ·· be a stationary sequence of random variables and E 1 , E 2 , · ··, EN mutually exclusive events defined on k consecutive X's such that the probabilities of the events have the sum unity. In the sequence E j1 , E j2 , · ·· generated by the X's, the mean waiting time from an event, say E j1 , to a repetition of that event is equal to N (under a mild condition of ergodicity). Applications are given.

How many random digits are required until given sequences are obtained?

1982 ◽  
Vol 19 (03) ◽  
pp. 518-531 ◽  
Author(s):  
Gunnar Blom ◽  
Daniel Thorburn
Keyword(s):  
Generating Function ◽  
Waiting Time ◽  
Probability Generating Function ◽  
Recursive Formula ◽  
Fixed Number ◽  
Digit Sequence ◽  
Mean Waiting Time ◽  
The Mean ◽  
The Given

Random digits are collected one at a time until a given k -digit sequence is obtained, or, more generally, until one of several k -digit sequences is obtained. In the former case, a recursive formula is given, which determines the distribution of the waiting time until the sequence is obtained and leads to an expression for the probability generating function. In the latter case, the mean waiting time is given until one of the given sequences is obtained, or, more generally, until a fixed number of sequences have been obtained, either different sequences or not necessarily different ones. Several results are known before, but the methods of proof seem to be new.

Limit theorem for continuous-time random walks with two time scales

2004 ◽  
Vol 41 (2) ◽  
pp. 455-466 ◽  
Author(s):  
Peter Becker-Kern ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Time Scales ◽  
Waiting Time ◽  
Continuous Time ◽  
Fractional Partial Differential Equations ◽  
Finite Dimensional ◽  
Mean Waiting Time ◽  
Continuous Time Random Walks ◽  
Random Jumps ◽  
The Mean

Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.

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