scholarly journals Some Results for Vacation Systems with Sojourn Time Limits

2011 ◽  
Vol 48 (3) ◽  
pp. 679-687 ◽  
Author(s):  
Tsuyoshi Katayama
Keyword(s):  
Steady State ◽  
Sojourn Time ◽  
Waiting Times ◽  
Level Crossing ◽  
Time Limits ◽  
Single Vacation ◽  
Vacation Time ◽  
Service Times ◽  
Constant Service Times ◽  
Explicit Expressions

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, explicit expressions for the steady-state distributions of the virtual waiting times are obtained in vacation systems with exponential and constant service times, a general vacation time, and two vacation rules.

scholarly journals Some Results for Vacation Systems with Sojourn Time Limits

2011 ◽  
Vol 48 (03) ◽  
pp. 679-687 ◽  
Author(s):  
Tsuyoshi Katayama
Keyword(s):  
Steady State ◽  
Sojourn Time ◽  
Waiting Times ◽  
Level Crossing ◽  
Time Limits ◽  
Single Vacation ◽  
Vacation Time ◽  
Service Times ◽  
Constant Service Times ◽  
Explicit Expressions

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, explicit expressions for the steady-state distributions of the virtual waiting times are obtained in vacation systems with exponential and constant service times, a general vacation time, and two vacation rules.

scholarly journals A Note on M/G/1 Vacation Systems with Sojourn Time Limits

2012 ◽  
Vol 49 (4) ◽  
pp. 1194-1199 ◽  
Author(s):  
Tsuyoshi Katayama
Keyword(s):  
Steady State ◽  
Sojourn Time ◽  
Waiting Times ◽  
Level Crossing ◽  
Time Limits ◽  
Single Vacation ◽  
Vacation Time ◽  
Recursive Equations

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, we derive recursive equations for the steady-state distributions of the virtual waiting times in M/G/1 vacation systems with a general vacation time and two vacation rules.

A Note on M/G/1 Vacation Systems with Sojourn Time Limits

2012 ◽  
Vol 49 (04) ◽  
pp. 1194-1199
Author(s):  
Tsuyoshi Katayama
Keyword(s):  
Steady State ◽  
Sojourn Time ◽  
Waiting Times ◽  
Level Crossing ◽  
Time Limits ◽  
Single Vacation ◽  
Vacation Time ◽  
Recursive Equations

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, we derive recursive equations for the steady-state distributions of the virtual waiting times in M/G/1 vacation systems with a general vacation time and two vacation rules.

Stochastic bounds for heterogeneous-server queues with Erlang service times

1974 ◽  
Vol 11 (04) ◽  
pp. 785-796 ◽  
Author(s):  
Oliver S. Yu
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Single Server ◽  
Shape Parameters ◽  
Server Queue ◽  
Service Times ◽  
Heavy Traffic Approximations ◽  
Multi Server

This paper establishes stochastic bounds for the phasal departure times of a heterogeneous-server queue with a recurrent input and Erlang service times. The multi-server queue is bounded by a simple GI/E/1 queue. When the shape parameters of the Erlang service-time distributions of different servers are the same, these relations yield two-sided bounds for customer waiting times and the queue length, which can in turn be used with known results for single-server queues to obtain characterizations of steady-state distributions and heavy-traffic approximations.

Stochastic bounds for heterogeneous-server queues with Erlang service times

1974 ◽  
Vol 11 (4) ◽  
pp. 785-796 ◽  
Author(s):  
Oliver S. Yu
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Single Server ◽  
Shape Parameters ◽  
Server Queue ◽  
Service Times ◽  
Heavy Traffic Approximations ◽  
Multi Server

This paper establishes stochastic bounds for the phasal departure times of a heterogeneous-server queue with a recurrent input and Erlang service times. The multi-server queue is bounded by a simple GI/E/1 queue. When the shape parameters of the Erlang service-time distributions of different servers are the same, these relations yield two-sided bounds for customer waiting times and the queue length, which can in turn be used with known results for single-server queues to obtain characterizations of steady-state distributions and heavy-traffic approximations.

On a tandem queueing model with identical service times at both counters, I

1979 ◽  
Vol 11 (3) ◽  
pp. 616-643 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Complete Analysis ◽  
Single Server ◽  
Stationary Distributions ◽  
In Series ◽  
Queues In Series ◽  
Service Times ◽  
Necessary And Sufficient ◽  
Insight Into

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process.Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue.In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

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.

The steady-state distribution of spent service times present in the M/G/1 foreground–background processor-sharing queue

1988 ◽  
Vol 25 (1) ◽  
pp. 194-203 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
Random Measure ◽  
Processor Sharing ◽  
Steady State Distribution ◽  
State Distribution ◽  
Generating Functional ◽  
Service Times

The steady-state distribution of spent service times present in the M/G/1 foreground-background processor-sharing queue is described by a random measure, whose generating functional is obtained.

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