scholarly journals Computational Analysis of Queues with Catastrophes in a Multiphase Random Environment

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
G. Arul Freeda Vinodhini ◽  
V. Vidhya
Keyword(s):  
Performance Measures ◽  
Computational Analysis ◽  
Road Traffic ◽  
Probability Generating Function ◽  
Weather Conditions ◽  
Traffic Model ◽  
Matrix Geometric Method ◽  
Special Cases ◽  
Full Capacity ◽  
Steady State Probabilities

A dynamically changing road traffic model which occasionally suffers a disaster (traffic collision, wrecked vehicles, conflicting weather conditions, spilled cargo, and hazardous matter) resulting in loss of all the vehicles (diverted to other routes) has been discussed. Once the system gets repaired, it undergoesn-1trial phases and finally reaches its full capacity phasen. We have obtained the explicit steady state probabilities of the system via Matrix Geometric Method. Probability Generating Function is used to evaluate the time spent by the system in each phase. Various performance measures like mean traffic, average waiting time of vehicles, and fraction of vehicles lost are calculated. Some special cases have also been discussed.

scholarly journals Analysis of an M/M/cQueueing System with Impatient Customers and Synchronous Vacations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Dequan Yue ◽  
Wuyi Yue ◽  
Guoxi Zhao
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Function Method ◽  
Queueing System ◽  
Probability Generating Function ◽  
Impatient Customers ◽  
Balance Equations ◽  
Limiting Behavior ◽  
Special Cases ◽  
Steady State Probabilities

We consider an M/M/cqueueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take another vacation; otherwise, they return to serve the queue. We develop the balance equations for the steady-state probabilities and solve the equations by using the probability generating function method. We obtain explicit expressions of some important performance measures by means of the two indexes. Based on these, we obtain some results about limiting behavior for some performance measures. We derive closed-form expressions of some important performance measures for two special cases. Finally, some numerical results are also presented.

A Novel Approach for Analyzing Single Buffer Queueing Systems with State-Dependent Vacation and Correlated Input Process under Four Different Service Disciplines

2015 ◽  
Vol 6 (3) ◽  
pp. 19-59 ◽  
Author(s):  
Thomas Yew Sing Lee
Keyword(s):  
Performance Measures ◽  
Probability Generating Function ◽  
Performance Measure ◽  
Idle Time ◽  
Separate Analysis ◽  
Input Process ◽  
State Dependent ◽  
Special Cases ◽  
Service Disciplines ◽  
Different Types

The author presents performance analysis of a single buffer multiple-queue system. Four different types of service disciplines (i.e., non-preemptive, pre-emptive repeat different, state dependent random polling and globally gated) are analyzed. His model includes correlated input process and three different types of non-productive time (i.e., switchover, vacation and idle time). Special cases of the model includes server with mixed multiple and single vacations, stopping server with delayed vacation and stopping server with alternating vacation and idle time. For each of the four service disciplines the key performance measures such as average customer waiting time, loss probability, and throughput are computed. The results permit a detailed discussion of how these performance measures depends on the customer arrival rate, the customer service time, the switchover time, the vacation time, and the idle time. Moreover, extensive numerical results are presented and the four service disciplines are compared with respect to the performance measure. Previous studies of the single buffer multiple-queue systems tend to provide separate analysis for the two cases of zero and nonzero switchover time. The author is able to provide a unified analysis for the two cases. His results generalize and improve a number of known results on single buffer multiple-queue systems. Furthermore, this method does not require differentiation while it is needed if one uses the probability generating function approach. Lastly, the author's approach works for all single buffer multiple-queue systems in which the next queue to be served is determines solely on the basis of the occupancy states at the end of the cycle time.

Convergence to equilibrium in a traffic model with restricted passing

1979 ◽  
Vol 16 (4) ◽  
pp. 881-889 ◽  
Author(s):  
Hans Dieter Unkelbach
Keyword(s):  
Poisson Process ◽  
Limit Theorems ◽  
Point Processes ◽  
Road Traffic ◽  
Poisson Processes ◽  
Traffic Model ◽  
Cluster Point ◽  
Convergence To Equilibrium ◽  
Constant Intensity

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes.The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.

scholarly journals Fluid Queue Driven by anM/M/1Queue Subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Kolinjivadi Viswanathan Vijayashree ◽  
Atlimuthu Anjuka
Keyword(s):  
Death Process ◽  
Queueing Model ◽  
Fluid Queue ◽  
Stationary Analysis ◽  
Governing System ◽  
Matrix Geometric Method ◽  
Vacation Interruption ◽  
Model Subject ◽  
Steady State Probabilities ◽  
Bernoulli Schedule

This paper deals with the stationary analysis of a fluid queue driven by anM/M/1queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

scholarly journals The truncated Hyper-Poisson queues: Hk/Ma,b/C/N with balking, reneging and general bulk service rule

2008 ◽  
Vol 18 (1) ◽  
pp. 23-36 ◽  
Author(s):  
A.I. Shawky ◽  
M.S. El-Paoumy
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Explicit Form ◽  
Recurrence Relations ◽  
Expected Number ◽  
Special Cases ◽  
Queue Discipline ◽  
Bulk Service ◽  
General Bulk Service Rule ◽  
Steady State Probabilities

The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained. .

scholarly journals Evaluation of possibilities for the climatic distribution of regions from the point of view of road construction

2015 ◽  
Vol 10 (3) ◽  
pp. 262-268 ◽  
Author(s):  
Lina Juknevičiūtė-Žilinskienė ◽  
Alfredas Laurinavičius
Keyword(s):  
Information System ◽  
Information Systems ◽  
Road Traffic ◽  
Road Construction ◽  
Weather Conditions ◽  
Frozen Ground ◽  
Weather Information ◽  
Road Pavement ◽  
The World ◽  
Pavement Structure

Seeking to reduce a negative impact of unfavourable weather conditions on road traffic, many countries introduce modern technologies allowing to objectively assessing meteorological conditions of roads. The world over, data from the automated meteorological stations of Road Weather Information System have been long ago used on a significantly larger scale than only for the organization of road maintenance works. International experience of introducing Road Traffic Information Systems in European Union and other countries of the world shows that Road Weather Information Systems give good results for increasing road safety, improving the level of road user information and solving the road construction issues. Road Weather Information System is a system of technologies and decision-making using historical and real-time data of roads and weather conditions. The collected and processed multi-year data from meteorological stations is a great assistance in designing or reconstructing road pavement structures. Road pavement structure is highly affected by a negative air temperature and frozen ground. The impact of negative temperature is expressed by the thickness of frost blanket course. The thickness of frost blanket course depends on a frost susceptibility of soil. To determine the thickness of frost blanket course it is necessary to assess the frost impact, therefore it was up to the purpose − climatic distribution of regions the territory of Lithuania according to the distribution of frost impact and the depth of frozen ground. Based on climatic maps compiled, a correction of the thickness of road pavement structure was suggested.

Formal Analysis of an Urban Road Traffic Model

2016 ◽  
pp. 533-544 ◽  
Author(s):  
Camelia Avram ◽  
Eduardo Valente ◽  
Adina Aştilean ◽  
José Machado ◽  
Dan Radu
Keyword(s):  
Road Traffic ◽  
Formal Analysis ◽  
Traffic Model ◽  
Urban Road

Yavuz Sultan Selim (3rd Bosphorus) Bridge-Inspection and Maintenance

2018 ◽  
Author(s):  
Abdul Farooq
Keyword(s):  
Health Monitoring ◽  
Bridge Deck ◽  
Road Traffic ◽  
Weather Conditions ◽  
Suspension Bridge ◽  
Bridge Inspection ◽  
Seismic Region ◽  
Inspection And Maintenance ◽  
Wind Climate ◽  
Heavy Rail

The Yavuz Sultan Selim bridge, also known as the 3rd Bosphorus Bridge, was opened to road traffic in August 2016. The stiffened suspension bridge, with a main span of 1408m, overall length 2250m and width 59.4m, is believed to be the first of its type. It is situated in a seismic region and exposed to a severe wind climate. It has been designed and constructed to carry 8 lanes of road traffic and twin track heavy rail-all on a single deck. <p> The bridge has been equipped with a Structural Health Monitoring (SHM) system. The instrumentation allows the monitoring of bridge behaviour. The dehumidification of the towers, bridge deck and suspension cables is also monitored. The ambient weather conditions including wind velocity, humidity and seismic activity are recorded. <p> This paper gives an overview of the inspection and maintenance regime. It also describes the observed performance of the bridge against its predicted behaviour.

Transient and steady-state analysis of a queuing system having customers’ impatience with threshold

2019 ◽  
Vol 53 (5) ◽  
pp. 1861-1876 ◽  
Author(s):  
Sapana Sharma ◽  
Rakesh Kumar ◽  
Sherif Ibrahim Ammar
Keyword(s):  
Steady State ◽  
Probability Generating Function ◽  
Threshold Value ◽  
Steady State Solution ◽  
Function Technique ◽  
Single Server ◽  
Queuing Model ◽  
Queuing Models ◽  
Special Cases ◽  
Number Of Customers

In many practical queuing situations reneging and balking can only occur if the number of customers in the system is greater than a certain threshold value. Therefore, in this paper we study a single server Markovian queuing model having customers’ impatience (balking and reneging) with threshold, and retention of reneging customers. The transient analysis of the model is performed by using probability generating function technique. The expressions for the mean and variance of the number of customers in the system are obtained and a numerical example is also provided. Further the steady-state solution of the model is obtained. Finally, some important queuing models are derived as the special cases of this model.

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