Response times in M/M/s fork-join networks

2004 ◽  
Vol 36 (3) ◽  
pp. 854-871 ◽  
Author(s):  
Sung-Seok Ko ◽  
Richard F. Serfozo
Keyword(s):  
Response Time ◽  
Poisson Process ◽  
Closed Form ◽  
Queue Length ◽  
Response Times ◽  
Statistical Tests ◽  
Queueing Systems ◽  
Kolmogorov Smirnov ◽  
Processing Network ◽  
Closed Form Formula

We study a fork-join processing network in which jobs arrive according to a Poisson process and each job splits into m tasks, which are simultaneously assigned to m nodes that operate like M/M/s queueing systems. When all of its tasks are finished, the job is completed. The main result is a closed-form formula for approximating the distribution of the network's response time (the time to complete a job) in equilibrium. We also present an analogous approximation for the distribution of the equilibrium queue length (the number of jobs in the system), when each node has one server. Kolmogorov-Smirnov statistical tests show that these formulae are good fits for the distributions obtained from simulations.

Response times in M/M/s fork-join networks

2004 ◽  
Vol 36 (03) ◽  
pp. 854-871 ◽  
Author(s):  
Sung-Seok Ko ◽  
Richard F. Serfozo
Keyword(s):  
Response Time ◽  
Poisson Process ◽  
Closed Form ◽  
Queue Length ◽  
Response Times ◽  
Statistical Tests ◽  
Queueing Systems ◽  
Kolmogorov Smirnov ◽  
Processing Network ◽  
Closed Form Formula

We study a fork-join processing network in which jobs arrive according to a Poisson process and each job splits into m tasks, which are simultaneously assigned to m nodes that operate like M/M/s queueing systems. When all of its tasks are finished, the job is completed. The main result is a closed-form formula for approximating the distribution of the network's response time (the time to complete a job) in equilibrium. We also present an analogous approximation for the distribution of the equilibrium queue length (the number of jobs in the system), when each node has one server. Kolmogorov-Smirnov statistical tests show that these formulae are good fits for the distributions obtained from simulations.

scholarly journals The effect of eight exercises on reaction and response times in older people

2020 ◽  
Author(s):  
Helia karimimoghadam ◽  
Mehrangiz Azmoun Cavan ◽  
Golaleh Karbasi
Keyword(s):  
Reaction Time ◽  
Older People ◽  
Response Time ◽  
Response Times ◽  
Physical Activities ◽  
Study Results ◽  
Independent Test ◽  
Kolmogorov Smirnov ◽  
Positive Effect ◽  
Inactive Group

Abstract Purpose the physical activities have a lot of effects on the improvement of cognitive and motor performance. The purpose of this study is to survey the effect of exercise and physical activities on the reaction and response times (or durations) in older people. Methodology: the method of the study is casual-comparative and its statistic society were consisted of older people of Sanandaj that among them, 30 inactive persons were randomly selected and 30 active and available persons were also selected and their reaction and response times were measured. The reaction time was measured by the reaction timer made by Takei Company (model YB1000) and response time was measured through the movement and response field test of Nelson's selection. The reaction time was firstly and then the response time was measured. For data analysis from the descriptive statistics, the K-S test and T- independent test were used. Results Kolmogorov - Smirnov test revealed that study results have normal distribution. According to the study results, exercise and physical activity have positive effect on reaction and response times so that the results of T independent test showed that the active group has meaningfully lower reaction time (P = 0.000) and response time (P = 0.0.000) than the inactive group. Conclusion the results of this study showed that exercise and physical activities lead to the decrement in reaction and response times through the positive physiological and psychomotor changes.

scholarly journals ON THE REPRESENTATION OF THE NESTED LOGIT MODEL

2021 ◽  
pp. 1-11
Author(s):  
Alfred Galichon
Keyword(s):  
Closed Form ◽  
Logit Model ◽  
Random Variables ◽  
Nested Logit ◽  
Random Utility ◽  
Nested Logit Model ◽  
Utility Representation ◽  
Phd Thesis ◽  
Closed Form Formula

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

Filtering of Markov renewal queues, IV: Flow processes in feedback queues

1985 ◽  
Vol 17 (2) ◽  
pp. 386-407 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Arrival Process ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Flow Process ◽  
Special Cases ◽  
Flow Processes ◽  
Transition Points ◽  
The Times

This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal kernel are derived, and thence expressions for the distribution of the times between transitions, under stationary conditions, are found for each of the above flow processes. In particular, it is shown that the inter-event distributions for the arrival process and the departure process are the same, with an equivalent result holding for inputs and outputs. Further, expressions for the stationary joint distributions of successive intervals between events in each flow process are derived and interconnections, using the concept of reversed Markov renewal processes, are explored. Conditions under which any of the flow processes are renewal processes or, more particularly, Poisson processes are also investigated. Special cases including, in particular, the M/M/1/N and M/M/1 model with instantaneous Bernoulli feedback, are examined.

Stationary Poisson departure processes from non-stationary queues

1986 ◽  
Vol 23 (1) ◽  
pp. 256-260 ◽  
Author(s):  
Robert D. Foley
Keyword(s):  
Poisson Process ◽  
Service Time ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Distribution Functions ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Departure Process ◽  
Infinite Server ◽  
Departure Processes

We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt/∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

Sign in / Sign up

Export Citation Format

Share Document