Mathematical Model of an Industrial Distributed Ledger as a Queueing System with Multiple Tickets of Unlimited Depth

2021 ◽  
Author(s):  
Vladimir Evsin ◽  
Svetlana Shirobokova ◽  
Sergei Vorobyev
Keyword(s):  
Mathematical Model ◽  
Queueing System ◽  
Distributed Ledger

scholarly journals Mathematical Models of Mb/M/1 Bulk Arrival Queueing System

2014 ◽  
Vol 10 (1) ◽  
pp. 184-191 ◽  
Author(s):  
Sushil Ghimire ◽  
R. P. Ghimire ◽  
Gyan Bahadur Thapa
Keyword(s):  
Mathematical Model ◽  
Function Method ◽  
Queueing System ◽  
Batch Size ◽  
Queueing Model ◽  
Mean Waiting Time ◽  
Bulk Arrival ◽  
Number Of Customers ◽  
The Mathematical Model ◽  
Mean Time

 This paper deals with the study of bulk queueing model with the fixed batch size ‘b’ and customers arrive to the system with Poisson fashion with the rate λ and are severed exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers/work pieces in the queue and in the system by using generating function method. Some numerical illustrations are also obtained by using MATLAB-7 so as to show the applicability of the model under study.DOI: http://dx.doi.org/10.3126/jie.v10i1.10899Journal of the Institute of Engineering, Vol. 10, No. 1, 2014, pp. 184–191

scholarly journals Multi-server queueing system with reserve servers

2019 ◽  
pp. 57-70
Author(s):  
Valentina I. Klimenok
Keyword(s):  
Mathematical Model ◽  
Energy Consumption ◽  
Service Time ◽  
Stochastic Systems ◽  
Queueing System ◽  
Arrival Process ◽  
Batch Markovian Arrival Process ◽  
Finite Set ◽  
And Performance ◽  
Multi Server

In this paper, we investigate a multi-server queueing system with an unlimited buffer, which can be used in the design of energy consumption schemes and as a mathematical model of unreliable real stochastic systems. Customers arrive to the system in a batch Markovian arrival process, the service times are distributed according to the phase law. If the service time of the customer by the server exceeds a certain random value distributed according to the phase law, this server receives assistance from the reserve server from a finite set of reserve servers. In the paper, we calculate the stationary distribution and performance characteristics of the system.

Constrained admission control to a queueing system

1989 ◽  
Vol 21 (2) ◽  
pp. 409-431 ◽  
Author(s):  
Arie Hordijk ◽  
Flos Spieksma
Keyword(s):  
Mathematical Model ◽  
Cost Function ◽  
Admission Control ◽  
Optimal Policy ◽  
Efficient Algorithm ◽  
Queueing System ◽  
Markov Decision ◽  
Service Rates ◽  
Good Policy ◽  
Proper Balance

We consider an exponential queue with arrival and service rates depending on the number of jobs present in the queue. The queueing system is controlled by restricting arrivals. Typically, a good policy should provide a proper balance between throughput and congestion. A mathematical model for computing such a policy is a Markov decision chain with rewards and a constrained cost function. We give general conditions on the reward and cost function which guarantee the existence of an optimal threshold or thinning policy. An efficient algorithm for computing an optimal policy is constructed.

scholarly journals M(t)/M/1 Queueing System with Sinusoidal Arrival Rate

2016 ◽  
Vol 11 (1) ◽  
pp. 120-127
Author(s):  
A. P. Pant ◽  
R. P. Ghimire
Keyword(s):  
Mathematical Model ◽  
Waiting Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Rate Function ◽  
Recursive Method ◽  
Mean Waiting Time ◽  
Number Of Customers ◽  
The Mathematical Model ◽  
Mean Time

This paper deals with the study of M (t)/M/1 queueing system with customers arrive to the system with sinusoidal arrival rate function λ (t) and are served exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers in the queue and in the system by using recursive method. Some numerical illustrations are also obtained by using computing software so as to show the applicability of the model under study.Journal of the Institute of Engineering, 2015, 11(1): 120-127

Constrained admission control to a queueing system

1989 ◽  
Vol 21 (02) ◽  
pp. 409-431 ◽  
Author(s):  
Arie Hordijk ◽  
Flos Spieksma
Keyword(s):  
Mathematical Model ◽  
Cost Function ◽  
Admission Control ◽  
Optimal Policy ◽  
Efficient Algorithm ◽  
Queueing System ◽  
Markov Decision ◽  
Service Rates ◽  
Good Policy ◽  
Proper Balance

We consider an exponential queue with arrival and service rates depending on the number of jobs present in the queue. The queueing system is controlled by restricting arrivals. Typically, a good policy should provide a proper balance between throughput and congestion. A mathematical model for computing such a policy is a Markov decision chain with rewards and a constrained cost function. We give general conditions on the reward and cost function which guarantee the existence of an optimal threshold or thinning policy. An efficient algorithm for computing an optimal policy is constructed.

scholarly journals Modelling of Freight Trains Classification Using Queueing System Subject to Breakdowns

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Michal Dorda ◽  
Dušan Teichmann
Keyword(s):  
Mathematical Model ◽  
Simulation Model ◽  
Petri Nets ◽  
Customer Service ◽  
Queueing System ◽  
Software Tool ◽  
Coloured Petri Nets ◽  
Marshalling Yard ◽  
The Mathematical Model

The paper presents a mathematical model and a simulation model of the freight trains classification process. We model the process as a queueing system with a server which is represented by a hump at a marshalling yard. We distinguish two types of shunting over the hump; primary shunting represents the classification of inbound freight trains over the hump (it is the primary function of marshalling yards), and secondary shunting is, for example, represented by the classification of trains of wagons entering the yard via industrial sidings. Inbound freight trains are considered to be customers in the system, and all needs of secondary shunting are failures of the hump because performing secondary shunting occupies the hump, and therefore inbound freight trains cannot be sorted. All random variables of the model are considered to be exponentially distributed with the exception of customer service times which are Erlang distributed. The mathematical model was created using method of stages and can be solved numerically employing a suitable software tool. The simulation model was created using coloured Petri nets. Both models are tested in conditions of a marshalling yard.

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