scholarly journals Dynamic Reliability of a Cluster Server

2016 ◽  
Vol 5 (4) ◽  
pp. 45
Author(s):  
Andrzej Korzeniowski ◽  
Rachel Traylor
Keyword(s):  
Poisson Process ◽  
Survival Function ◽  
Channel Selection ◽  
Single Server ◽  
Numerical Comparison ◽  
Constant Multiple ◽  
Dynamic Reliability ◽  
K Channels ◽  
Correlated Channels ◽  
The Relationship

Suppose a single server has $K$ channels, each of which performs a different task. Customers arrive to the server via a nonhomogenous Poisson process with intensity $\lambda(t)$ and select $0$ to $K$ tasks for the server to perform. Each channel services the tasks in its queue independently, and the customer's job is complete when the last task selected is complete. The stress to the server is a constant multiple $\eta$ of the number of tasks selected by each customer, and thus the stress added to the server by each customer is random. Under this model, we provide the survival function for such a server in both the case of independently selected channels and correlated channels. A numerical comparison of expected lifetimes for various arrival rates is given, and the relationship between the dependency of channel selection and expected server lifetime is presented.

The depletion time for M/G/1 systems and a related limit theorem

1983 ◽  
Vol 15 (02) ◽  
pp. 420-443 ◽  
Author(s):  
Julian Keilson ◽  
Ushio Sumita
Keyword(s):  
Limit Theorem ◽  
Time Distribution ◽  
Numerical Evaluation ◽  
Heavy Traffic ◽  
Single Server ◽  
Service Time Distribution ◽  
Traffic Intensity ◽  
Traffic Distribution ◽  
Delay Times ◽  
The Relationship

Waiting-time distributions for M/G/1 systems with priority dependent on class, order of arrival, service length, etc., are difficult to obtain. For single-server multipurpose processors the difficulties are compounded. A certain ergodic post-arrival depletion time is shown to be a true maximum for all delay times of interest. Explicit numerical evaluation of the distribution of this time is available. A heavy-traffic distribution for this time is shown to provide a simple and useful engineering tool with good results and insensitivity to service-time distribution even at modest traffic intensity levels. The relationship to the diffusion approximation for heavy traffic is described.

scholarly journals Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula

2019 ◽  
Vol 29 (8) ◽  
pp. 2307-2327 ◽  
Author(s):  
Takeshi Emura ◽  
Jia-Han Shih ◽  
Il Do Ha ◽  
Ralf A Wilke
Keyword(s):  
Competing Risks ◽  
Hazard Function ◽  
Cox Regression ◽  
Cox Model ◽  
Hazard Model ◽  
Numerical Comparison ◽  
Hazard Functions ◽  
Different Types ◽  
Competing Risks Data ◽  
The Relationship

For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (1) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation.Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

Approximations for delays using asymptotic estimates

1984 ◽  
Vol 16 (01) ◽  
pp. 6
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Heavy Traffic ◽  
Single Server ◽  
Asymptotic Estimates ◽  
Single Server Queue ◽  
Average Delay ◽  
Multiserver Queues ◽  
Server Queue

Consider a general single-server queue where the customers arrive according to a Poisson process whose rate is modulated according to an independent Markov process. The authors have previously reported on limits for the average delay in light and heavy traffic. In this paper we review these results, extend them to multiserver queues, and describe some approximations obtained from them for general delays.

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (4) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

scholarly journals Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

2020 ◽  
Vol 20 (4) ◽  
pp. 534-547
Author(s):  
Ekaterina A. Fedorova ◽  
◽  
Anatoly A. Nazarov ◽  
Mais P. Farkhadov ◽  
◽  
...  
Keyword(s):  
Asymptotic Analysis ◽  
Retrial Queue ◽  
Load Condition ◽  
System Capacity ◽  
Stationary Mode ◽  
Single Server ◽  
Numerical Comparison ◽  
Heavy Load ◽  
Retrial Queueing System ◽  
Asymptotic Characteristic

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed. It is proved that the asymptotic characteristic function of a number of calls on the orbit has the gamma distribution with the obtained parameters. The value of the system capacity is obtained, so, the condition of the system stationary mode is found. The results of a numerical comparison of the asymptotic distribution and the distribution obtained by simulation are presented. Conclusions about the method applicability area are made.

scholarly journals Study on reservoir time-varying design flood of inflow based on Poisson process with time-dependent parameters

2018 ◽  
Vol 379 ◽  
pp. 119-123
Author(s):  
Jiqing Li ◽  
Jing Huang ◽  
Jianchang Li
Keyword(s):  
Poisson Process ◽  
Flood Control ◽  
Time Dependent ◽  
Model Parameters ◽  
Time Varying ◽  
Design Flood ◽  
Threshold Method ◽  
Peak Over Threshold ◽  
Peak Over Threshold Method ◽  
The Relationship

Abstract. The time-varying design flood can make full use of the measured data, which can provide the reservoir with the basis of both flood control and operation scheduling. This paper adopts peak over threshold method for flood sampling in unit periods and Poisson process with time-dependent parameters model for simulation of reservoirs time-varying design flood. Considering the relationship between the model parameters and hypothesis, this paper presents the over-threshold intensity, the fitting degree of Poisson distribution and the design flood parameters are the time-varying design flood unit period and threshold discriminant basis, deduced Longyangxia reservoir time-varying design flood process at 9 kinds of design frequencies. The time-varying design flood of inflow is closer to the reservoir actual inflow conditions, which can be used to adjust the operating water level in flood season and make plans for resource utilization of flood in the basin.

scholarly journals Heavy outgoing call asymptotics for retrial queue with two way communication and multiple types of outgoing calls

2019 ◽  
Vol 27 (1) ◽  
pp. 5-20
Author(s):  
Anatoly A Nazarov ◽  
Svetlana V Paul ◽  
Olga D Lizyura
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Service Time ◽  
Retrial Queue ◽  
Idle Time ◽  
Single Server ◽  
Queueing Model ◽  
Exponential Distributions ◽  
Incoming Call

In this paper, we consider a single server queueing model M |M |1|N with two types of calls: incoming calls and outgoing calls, where incoming calls arrive at the server according to a Poisson process. Upon arrival, an incoming call immediately occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing calls after an exponentially distributed idle time. It can be interpreted as that outgoing calls arrive at the server according to a Poisson process. There are N types of outgoing calls whose durations follow N distinct exponential distributions. Our contribution is to derive the asymptotics of the number of incoming calls in retrial queue under the conditions of high rates of making outgoing calls and low rates of service time of each type of outgoing calls. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of incoming calls in the system.

Single-Server Queue System of Shuttle Bus Performance: Federal University of Technology Akure as Case Study

2019 ◽  
Vol 5 (3) ◽  
pp. 9-14
Author(s):  
Sidiq Okwudili Ben
Keyword(s):  
Laplace Transform ◽  
Poisson Process ◽  
Service Rate ◽  
Single Server ◽  
Single Server Queue ◽  
Queue System ◽  
University Of Technology ◽  
Server Queue

This study has examined the performance of University transport bus shuttle based on utilization using a Single-server queue system which occur if arrival and service rate is Poisson distributed (single queue) (M/M/1) queue. In the methodology, Single-server queue system was modelled based on Poisson Process with the introduction of Laplace Transform. It is concluded that the performance of University transport bus shuttle is 96.6 percent which indicates a very good performance such that the supply of shuttle bus in FUTA is capable of meeting the demand.

Average delay in queues with non-stationary Poisson arrivals

1978 ◽  
Vol 15 (03) ◽  
pp. 602-609 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Poisson Process ◽  
Intensity Function ◽  
Arrival Process ◽  
Single Server ◽  
Actual Process ◽  
Average Delay ◽  
Average Value ◽  
Poisson Arrival ◽  
Poisson Arrivals ◽  
Customer Delay

One of the major difficulties in attempting to apply known queueing theory results to real problems is that almost always these results assume a time-stationary Poisson arrival process, whereas in practice the actual process is almost invariably non-stationary. In this paper we consider single-server infinite-capacity queueing models in which the arrival process is a non-stationary process with an intensity function ∧(t), t ≧ 0, which is itself a random process. We suppose that the average value of the intensity function exists and is equal to some constant, call it λ, with probability 1. We make a conjecture to the effect that ‘the closer {∧(t), t ≧ 0} is to the stationary Poisson process with rate λ ' then the smaller is the average customer delay, and then we verify the conjecture in the special case where the arrival process is an interrupted Poisson process.

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