Theoretical solutions for degree distribution of decreasing random birth-and-death networks

2017 ◽  
Vol 31 (14) ◽  
pp. 1750161 ◽  
Author(s):  
Yin Long ◽  
Xiao-Jun Zhang ◽  
Kui Wang
Keyword(s):  
Steady State ◽  
Computer Simulations ◽  
Generating Function ◽  
Degree Distribution ◽  
Probability Generating Function ◽  
Function Approach ◽  
Poisson Summation

In this paper, theoretical solutions for degree distribution of decreasing random birth-and-death networks [Formula: see text] are provided. First, we prove that the degree distribution has the form of Poisson summation, for which degree distribution equations under steady state and probability generating function approach are employed. Then, based on the form of Poisson summation, we further confirm the tail characteristic of degree distribution is Poisson tail. Finally, simulations are carried out to verify these results by comparing the theoretical solutions with computer simulations.

A queue with Markov-dependent service times

1968 ◽  
Vol 5 (02) ◽  
pp. 461-466
Author(s):  
Gerold Pestalozzi
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Queueing System ◽  
Single Channel ◽  
Probability Generating Function ◽  
Average Waiting Time ◽  
Poisson Input ◽  
The Mean

A queueing system is considered where each item has a property associated with it, and where the service time interposed between two items depends on the properties of both of these items. The steady state of a single-channel queue of this type, with Poisson input, is investigated. It is shown how the probability generating function of the number of items waiting can be found. Easily applied approximations are given for the mean number of items waiting and for the average waiting time.

Queuing Scheme with Feedback Service and Discretionary Administration

2019 ◽  
Vol 9 (1S4) ◽  
pp. 706-710 ◽  
Keyword(s):  
Generating Function ◽  
Average Length ◽  
Probability Generating Function ◽  
Function Approach ◽  
Single Server ◽  
Queue Size ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Supplementary Variable Technique ◽  
Central Organization

This article take a gander at a bunch area single server channel Queuing system, where the server gives two sorts of organizations viz., beginning one a central organization and the optional organization is permitted as a second organization. In case in need, the customer settle on the optional organization .We other than anticipate that after the execution of the second time of affiliation, if the structure is unfilled, the server takes a required get-away of general dissemination. Organization thwarts in the midst of principal organization at random. Additionally if the customer isn't satisfied with the primary central organization, an info advantage for the proportionate is given to make a worthy space for the customers in the system. For the above delineated covering issue, the supplementary variable technique and generating function approach are used to derive the probability generating function of the queue size and the average length of the queue.

On a non-Markovian time-dependent queueing system

1989 ◽  
Vol 26 (1) ◽  
pp. 142-151 ◽  
Author(s):  
S. D. Sharma
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Transient State ◽  
Time Dependent ◽  
Queue Length Distribution ◽  
State Behaviour

This paper studies the transient and steady-state behaviour of a continuous and discrete-time queueing system with non-Markovian type of departure mechanism. The Laplace transforms of the probability generating function of the time-dependent queue length distribution in the transient state are obtained and the probability generating function of the queue length distribution in the steady state is derived therefrom. Finally, some particular cases are discussed.

On a non-Markovian time-dependent queueing system

1989 ◽  
Vol 26 (01) ◽  
pp. 142-151
Author(s):  
S. D. Sharma
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Transient State ◽  
Time Dependent ◽  
Queue Length Distribution ◽  
State Behaviour

This paper studies the transient and steady-state behaviour of a continuous and discrete-time queueing system with non-Markovian type of departure mechanism. The Laplace transforms of the probability generating function of the time-dependent queue length distribution in the transient state are obtained and the probability generating function of the queue length distribution in the steady state is derived therefrom. Finally, some particular cases are discussed.

scholarly journals Reservicing some customers inM/G/1queues under three disciplines

2004 ◽  
Vol 2004 (32) ◽  
pp. 1715-1723 ◽  
Author(s):  
M. R. Salehi-Rad ◽  
K. Mengersen ◽  
G. H. Shahkar
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Production Line ◽  
Busy Period ◽  
Probability Generating Function ◽  
Idle Period ◽  
The Mean ◽  
The Moment ◽  
State Size

Consider anM/G/1production line in which a production item is failed with some probability and is then repaired. We consider three repair disciplines depending on whether the failed item is repaired immediately or first stockpiled and repaired after all customers in the main queue are served or the stockpile reaches a specified threshold. For each discipline, we find the probability generating function (p.g.f.) of the steady-state size of the system at the moment of departure of the customer in the main queue, the mean busy period, and the probability of the idle period.

DISTRIBUTION DYNAMICS FOR SIS MODEL ON RANDOM NETWORKS

2012 ◽  
Vol 20 (02) ◽  
pp. 213-220 ◽  
Author(s):  
YILUN SHANG
Keyword(s):  
Generating Function ◽  
Degree Distribution ◽  
Probability Generating Function ◽  
Configuration Model ◽  
Random Networks ◽  
Distribution Dynamics ◽  
Sis Model ◽  
Function Formalism

We study the evolution of degree distributions of susceptible-infected-susceptible (SIS) model on random networks, where susceptible nodes are capable of being infected, and infected nodes can spread the disease further. The network of contacts is modeled as a configuration model featuring heterogeneous degree distribution. We derive systematically the (excess) degree distributions among susceptible and infected individuals by using the probability generating function formalism.

A queue with Markov-dependent service times

1968 ◽  
Vol 5 (2) ◽  
pp. 461-466 ◽  
Author(s):  
Gerold Pestalozzi
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Queueing System ◽  
Single Channel ◽  
Probability Generating Function ◽  
Average Waiting Time ◽  
Poisson Input ◽  
The Mean

A queueing system is considered where each item has a property associated with it, and where the service time interposed between two items depends on the properties of both of these items. The steady state of a single-channel queue of this type, with Poisson input, is investigated. It is shown how the probability generating function of the number of items waiting can be found. Easily applied approximations are given for the mean number of items waiting and for the average waiting time.

scholarly journals Effects of Catastrophe on a Queueing System with Voice over Internet Protocol

2019 ◽  
Vol 8 (4) ◽  
pp. 7301-7305
Keyword(s):  
Steady State ◽  
Size Distribution ◽  
Generating Function ◽  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
System Size ◽  
Voice Over Internet Protocol ◽  
Multiple Vacation ◽  
Heterogeneous Services

Consider a retrial queue with VoIP calls and two kinds of heterogeneous services such as essential and optional services. The multiple vacation policy, retrial policy, customer’s impatience and the concept of catastrophe are adopted to derive the required solutions. The steady state system size distribution and probability generating function under different level have been obtained. Based on some assumptions, special and particular cases are discussed.

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