s-expected number of inspections and repairs of a single server n-unit system subject to arbitrary failure

1984 ◽  
Vol 24 (4) ◽  
pp. 651-658 ◽  
Author(s):  
R. Subramanyam Naidu ◽  
M.N. Gopalan
Keyword(s):  
Single Server ◽  
Expected Number ◽  
Unit System

On queueing systems by retrials

1983 ◽  
Vol 20 (02) ◽  
pp. 380-389 ◽  
Author(s):  
Vidyadhar G. Kulkarni
Keyword(s):  
General Result ◽  
Service Time ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Waiting Room ◽  
Second Moments ◽  
Different Types ◽  
General Distributions ◽  
Arbitrary Service Time

A general result for queueing systems with retrials is presented. This result relates the expected total number of retrials conducted by an arbitrary customer to the expected total number of retrials that take place during an arbitrary service time. This result is used in the analysis of a special system where two types of customer arrive in an independent Poisson fashion at a single-server service station with no waiting room. The service times of the two types of customer have independent general distributions with finite second moments. When the incoming customer finds the server busy he immediately leaves and tries his luck again after an exponential amount of time. The retrial rates are different for different types of customers. Expressions are derived for the expected number of retrial customers of each type.

scholarly journals Applications of Queuing Theory in Quantitative Business Analysis

2020 ◽  
pp. 253-257
Keyword(s):  
Quantitative Analysis ◽  
Waiting Time ◽  
Queuing Theory ◽  
Single Channel ◽  
Analysis Approach ◽  
Single Server ◽  
Expected Number ◽  
Queuing Model ◽  
Infinite Population ◽  
Expected Waiting Time

Queuing Theory provides the system of applications in many sectors in life cycle. Queuing Structure and basic components determination is computed in queuing model simulation process. Distributions in Queuing Model can be extracted in quantitative analysis approach. Differences in Queuing Model Queue discipline, Single and Multiple service station with finite and infinite population is described in Quantitative analysis process. Basic expansions of probability density function, Expected waiting time in queue, Expected length of Queue, Expected size of system, probability of server being busy, and probability of system being empty conditions can be evaluated in this quantitative analysis approach. Probability of waiting ‘t’ minutes or more in queue and Expected number of customer served per busy period, Expected waiting time in System are also computed during the Analysis method. Single channel model with infinite population is used as most common case of queuing problems which involves the single channel or single server waiting line. Single Server model with finite population in test statistics provides the Relationships used in various applications like Expected time a customer spends in the system, Expected waiting time of a customer in the queue, Probability that there are n customers in the system objective case, Expected number of customers in the system

scholarly journals Cost -Benefit Analysis of a Single-Unit System with Preventive Maintenance and Weibull Distribution for Failure and Repair Activities

2014 ◽  
Vol 10 (2) ◽  
pp. 5-19 ◽  
Author(s):  
Ashish Kumar ◽  
Monika Saini
Keyword(s):  
Preventive Maintenance ◽  
Single Unit ◽  
Failure Time ◽  
Cost Benefit Analysis ◽  
Cost Benefit ◽  
Single Server ◽  
Scale Parameters ◽  
Unit System ◽  
Complete Failure ◽  
Replacement Time

Abstract This paper deals with a reliability model developed for a single-unit system which goes for preventive maintenance after a pre-specific time ‘t’ up to which no failure occurs. There is a single server who takes some time to arrive at the system for doing repair activities. The unit does not work as new after repair at complete failure and so called the degraded unit. The degraded unit is replaced by new one after its failure with some replacement time. The failure time, preventive maintenance time, replacement time and repair time of the unit are taken as Weibull distributed with common shape parameter and different scale parameters. The switching devices are perfect. The system is observed at suitable regenerative epochs to obtain various measures of system effectiveness of interest to system designers and operation managers.

scholarly journals Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
K. V. Abdul Rasheed ◽  
M. Manoharan
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Multiple Servers ◽  
Special Cases ◽  
Service Rates ◽  
Expected Waiting Time ◽  
Number Of Customers ◽  
Steady State Probabilities

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service ratesμ1,μ2, andμ(μ1≤μ2<μ), say, slow, medium, and fast rates, respectively. If the number of customers in the system exceeds a particular pointK1orK2, the server switches to the medium or fast rate, respectively. For this adaptive queueing system the steady state probabilities are derived and some performance measures such as expected number in the system/queue and expected waiting time in the system/queue are obtained. Multiple server discouraged arrival model having one service switch and single server discouraged arrival model having one and two service switches are obtained as special cases. A Matlab program of the model is presented and numerical illustrations are given.

On queueing systems by retrials

1983 ◽  
Vol 20 (2) ◽  
pp. 380-389 ◽  
Author(s):  
Vidyadhar G. Kulkarni
Keyword(s):  
General Result ◽  
Service Time ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Waiting Room ◽  
Second Moments ◽  
Different Types ◽  
General Distributions ◽  
Arbitrary Service Time

A general result for queueing systems with retrials is presented. This result relates the expected total number of retrials conducted by an arbitrary customer to the expected total number of retrials that take place during an arbitrary service time. This result is used in the analysis of a special system where two types of customer arrive in an independent Poisson fashion at a single-server service station with no waiting room. The service times of the two types of customer have independent general distributions with finite second moments. When the incoming customer finds the server busy he immediately leaves and tries his luck again after an exponential amount of time. The retrial rates are different for different types of customers. Expressions are derived for the expected number of retrial customers of each type.

The departure process of the M/G/1 queueing model with server vacation and exhaustive service discipline

1994 ◽  
Vol 31 (4) ◽  
pp. 1070-1082 ◽  
Author(s):  
Yinghui Tang
Keyword(s):  
Renewal Theory ◽  
Service Discipline ◽  
Time Interval ◽  
Single Server ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Departure Process ◽  
Server Vacation ◽  
Server Queue ◽  
Interdeparture Time

In this paper we study the departure process of M/G/1 queueing models with a single server vacation and multiple server vacations. The arguments employed are direct probability decomposition, renewal theory and the Laplace–Stieltjes transform. We discuss the distribution of the interdeparture time and the expected number of departures occurring in the time interval (0, t] from the beginning of the state i (i = 0, 1, 2, ···), and provide a new method for analysis of the departure process of the single-server queue.

Losses per cycle in a single-server queue

2002 ◽  
Vol 39 (04) ◽  
pp. 905-909 ◽  
Author(s):  
Ronald W. Wolff
Keyword(s):  
Elementary Proof ◽  
Arbitrary Order ◽  
Batch Size ◽  
Single Server ◽  
Expected Number ◽  
Batch Arrivals ◽  
Service Interruption ◽  
Server Queue ◽  
Service Rates ◽  
Busy Cycle

Several recent papers have shown that for the M/G/1/n queue with equal arrival and service rates, the expected number of lost customers per busy cycle is equal to 1 for every n ≥ 0. We present an elementary proof based on Wald's equation and, for GI/G/1/n, obtain conditions for this quantity to be either less than or greater than 1 for every n ≥ 0. In addition, we extend this result to batch arrivals, where, for average batch size β, the same quantity is either less than or greater than β. We then extend these results to general ways that customers may be lost, to an arbitrary order of service that allows service interruption, and finally to reneging.

scholarly journals Covert Cycle Stealing in a Single FIFO Server

2021 ◽  
Vol 6 (2) ◽  
pp. 1-33
Author(s):  
Bo Jiang ◽  
Philippe Nain ◽  
Don Towsley
Keyword(s):  
Phase Transition ◽  
Fisher Information ◽  
Single Server ◽  
Expected Number ◽  
General Service Times ◽  
Poisson Stream ◽  
Service Times ◽  
First In First Out ◽  
To Receive ◽  
General Service

Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: What is the number of jobs that she can receive covertly, i.e., without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates μ 1 and μ 2 , we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles: over n busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of O (√ n ) when μ 1 < 2 μ 2 , O (√ n log n ) when μ 1 = 2μ 2 , and O ( n μ 2 /μ 1 ) when μ 1 > 2μ 2 . When both Willie and Alice jobs have general service times, we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.

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