scholarly journals Analysis of a production system with a feedback buffer and a general dispatching time

2000 ◽  
Vol 5 (5) ◽  
pp. 421-439 ◽  
Author(s):  
Ho Woo Lee ◽  
Boo Yong Ahn
Keyword(s):  
Performance Measures ◽  
Production System ◽  
Sojourn Time ◽  
Operating Cost ◽  
Buffer Size ◽  
General Distribution ◽  
The Mean

In this paper, we analyze a production system with a finite feedback buffer and dispatching time. Parts enter a “main buffer” before they are processed. Processed parts leave the system with probability1−por are fed back to a “feedback buffer” with probabilityp. As soon as the feedback buffer becomes full, the parts in the feedback buffer are dispatched, all at once, to the main buffer by the server for reprocessing. The dispatching time follows a general distribution. Thus the server is engaged either in one of the following states: idle, processing, dispatching.We derive various performance measures such as the mean number of parts in each buffer, the mean system sojourn time and the dispatching rate. We also discuss the effects of the dispatching time on the performance measures. We finally derive the procedure to obtain the optimal buffer size that minimizes the overall operating cost.

The disasters queue with working breakdowns and impatient customers

2020 ◽  
Vol 54 (3) ◽  
pp. 815-825
Author(s):  
Mian Zhang ◽  
Shan Gao
Keyword(s):  
Size Distribution ◽  
Performance Measures ◽  
Sojourn Time ◽  
Queue Length ◽  
Slow Rate ◽  
System Size ◽  
Impatient Customers ◽  
Numerical Examples ◽  
The Mean ◽  
Mean Queue Length

We consider the M/M/1 queue with disasters and impatient customers. Disasters only occur when the main server being busy, it not only removes out all present customers from the system, but also breaks the main server down. When the main server is down, it is sent for repair. The substitute server serves the customers at a slow rate(working breakdown service) until the main server is repaired. The customers become impatient due to the working breakdown. The system size distribution is derived. We also obtain the mean queue length of the model and mean sojourn time of a tagged customer. Finally, some performance measures and numerical examples are presented.

scholarly journals Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule

2016 ◽  
Vol 4 (6) ◽  
pp. 547-559
Author(s):  
Jingjing Ye ◽  
Liwei Liu ◽  
Tao Jiang
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Sojourn Time ◽  
Time Distribution ◽  
Busy Period ◽  
Balance Equations ◽  
Sojourn Time Distribution ◽  
The Mean ◽  
System Length ◽  
Number Of Customers

AbstractThis paper studies a single-sever queue with disasters and repairs, in which after each service completion the server may take a vacation with probabilityq(0≤q≤1), or begin to serve the next customer, if any, with probabilityp(= 1− q). The disaster only affects the system when the server is in operation, and once it occurs, all customers present are eliminated from the system. We obtain the stationary probability generating functions (PGFs) of the number of customers in the system by solving the balance equations of the system. Some performance measures such as the mean system length, the probability that the server is in different states, the rate at which disasters occur and the rate of initiations of busy period are determined. We also derive the sojourn time distribution and the mean sojourn time. In addition, some numerical examples are presented to show the effect of the parameters on the mean system length.

Lambing season and fertility of fat-tailed ewes under an extensive production system are associated with liveweight and body condition around mating

2009 ◽  
Vol 49 (12) ◽  
pp. 1086 ◽  
Author(s):  
A. K. Esmailizadeh ◽  
O. Dayani ◽  
M. S. Mokhtari
Keyword(s):  
Body Condition ◽  
Production System ◽  
Fixed Effects ◽  
Body Condition Score ◽  
Mating Period ◽  
Breed Group ◽  
Significant Difference ◽  
Condition Score ◽  
The Mean ◽  
June July

The objective of this study was to investigate to what extent fertility and lambing season of fat-tailed ewes raised under an extensive production system are related to liveweight, body condition and changes around mating. Ewe liveweight and body condition score (BSC) were recorded in June, July and August over a period of 3 years (1999–2001) in 11 flocks (eight flocks of Kurdi breed and three flocks of Kurdi × Sanjabi crossbred). Both Kurdi and Sanjabi are native fat-tailed breeds in western Iran. In total, 3278 lambing records relating to 1592 ewes and data on mating date, liveweight and BCS of 1930 ewes (3975 records) were used for statistical analyses. The statistical model for bodyweight and body condition data included fixed effects of breed group, flock nested within breed group, year, the future lambing status following summer breeding (barren, autumn lambing and winter lambing), ewe age and all two-way interactions. Breed group had a significant effect on ewe liveweight (P < 0.01). However, there was no significant difference between BCS of the two breed groups around mating. Ewe liveweights measured in June, July and August had significant effects on fertility and lambing season (P < 0.01). Ewes that produced lambs were generally heavier at mating than barren ewes (P < 0.01). Autumn-lambing ewes were heavier than winter-lambing ewes in June and July (P < 0.01). Effects of changes in liveweight on fertility and lambing season were significant (P < 0.01). The effects of BCS in June, July and August (P < 0.01) and changes in BCS during the mating period (P < 0.05) on fertility and lambing season were also significant. The mean BCS (in June and July) of autumn-lambing ewes was greater than that of the winter-lambing and barren ewes (P < 0.05). The proportion of autumn-lambing ewes significantly increased as BCS in July increased, whereas the proportion of barren ewes decreased (P < 0.01). Fertility was associated with age so that as the age of the ewes increased from 2 to 7 years, the proportion of barren ewes significantly decreased from 29 to 5% (P < 0.01). There was a relatively high proportion of very thin ewes of 2 and 3 years of age. These findings imply that low body condition is a particular problem in younger ewes suggesting the importance of giving special nutritional treatment to younger ewes to reduce the proportion of barren ewes.

Single-Subgroup Performance Measures and Diagnostic Procedures for X-Bar Control Charts

1994 ◽  
Vol 116 (2) ◽  
pp. 216-224
Author(s):  
G. E. Rahn ◽  
S. G. Kapoor ◽  
R. E. DeVor
Keyword(s):  
Performance Measures ◽  
Control Charts ◽  
Simulated Data ◽  
Diagnostic Procedures ◽  
Shewhart Control Charts ◽  
Operational Characteristics ◽  
Shewhart Control ◽  
The Mean ◽  
Measures Of Performance ◽  
Tremendous Impact

Although Shewhart control charts have had a tremendous impact on quality improvement, the inability to precisely measure chart performance has limited their role, and subsequently overall effectiveness in the control of manufacturing processes. Measures of performance in terms of operational characteristics (OC) are defined on two distinct levels: (a) single-subgroup level, which examines the probability of a rule violation at any given subgroup (b) multiple-subgroup level, which considers the probability of one or more rule violations throughout process monitoring. Single-subgroup performance measures for X-bar charts that employ four rules are formulated. These measures are exact expressions of operational characteristics, except for the numerical approximation to the integral of the normal distribution. Applications of these models to simulated data demonstrate their accuracy in predicting chart performance. In addition, a diagnostic methodology is described which utilizes the derived performance measures to predict the mean of a shifted distribution. The proposed diagnostic procedure is illustrated in validation and application examples.

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.

Analysis of the fluid weighted fair queueing system

2003 ◽  
Vol 40 (1) ◽  
pp. 180-199 ◽  
Author(s):  
Fabrice Guillemin ◽  
Ravi Mazumdar ◽  
Alain Dupuis ◽  
Jacqueline Boyer
Keyword(s):  
Laplace Transform ◽  
Performance Measures ◽  
Joint Distribution ◽  
Queueing System ◽  
Laplace Transforms ◽  
Fair Queueing ◽  
Mean Waiting Time ◽  
The Laplace Transform ◽  
The Mean

We analyse in this paper the fluid weighted fair queueing system with two classes of customers, who arrive according to Poisson processes and require arbitrarily distributed service times. In a first step, we express the Laplace transform of the joint distribution of the workloads in the two virtual queues of the system by means of unknown Laplace transforms. Such an unknown Laplace transform is related to the distribution of the workload in one queue provided that the other queue is empty. We explicitly compute the unknown Laplace transforms by means of a Wiener—Hopf technique. The determination of the unknown Laplace transforms can be used to compute some performance measures characterizing the system (e.g. the mean waiting time for each class) which we compute in the exponential service case.

APPROXIMATION OF PH/PH/c RETRIAL QUEUE WITH PH-RETRIAL TIME

2014 ◽  
Vol 31 (02) ◽  
pp. 1440010 ◽  
Author(s):  
YANG WOO SHIN ◽  
DUG HEE MOON
Keyword(s):  
Time Distribution ◽  
Retrial Queue ◽  
Retrial Queues ◽  
General Distribution ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Phase Type ◽  
Sojourn Time Distribution ◽  
The Mean ◽  
Number Of Customers

We consider the PH/PH/c retrial queues with PH-retrial time. Approximation formulae for the distribution of the number of customers in service facility, sojourn time distribution and the mean number of customers in orbit are presented. We provide an approximation for GI/G/c retrial queue with general retrial time by approximating the general distribution with phase type distribution. Some numerical results are presented.

scholarly journals A fluid queue with a finite buffer and subexponential input

2000 ◽  
Vol 32 (1) ◽  
pp. 221-243 ◽  
Author(s):  
A. P. Zwart
Keyword(s):  
Stationary Distribution ◽  
Fluid Model ◽  
Buffer Size ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Buffer Content ◽  
The Mean ◽  
Heavy Tailed ◽  
Finite Dam

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

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