Queuing Theory of Improved Practical Byzantine Fault Tolerant Consensus

In recent years, the use of consensus mechanism to maintain the security of blockchain system has become a considerable concern of the community. Delegated proof of stake (DPoS) and practical Byzantine fault tolerant (PBFT) consensus mechanisms are key technologies in maintaining the security of blockchain system. First, this study proposes a consensus mechanism combining DPoS and PBFT, which can rapidly deal with malicious witness nodes and shorten the time of block verification. Second, the M/PH/1 queuing model is used to analyze the performance of the proposed consensus mechanism, and the performance of the improved practical Byzantine fault tolerant consensus mechanism is evaluated from steady-state conditions and key performance measure of the system. Third, the current study uses the theoretical method of open (Jackson) queuing network, combined with the blockchain consensus process, and provides theoretical analysis with special cases. Lastly, this research utilizes numerical examples to verify the computability of the theoretical results. The analytic method is expected to open a series of potentially promising research in queueing theory of blockchain systems.

Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit

We link the Brownian non-Gaussian diffusion of a polymer center of mass to a microscopic cause: the polymerization/depolymerization phenomenon occurring when the polymer is in contact with a monomer chemostat. The anomalous behavior is triggered by the polymer critical point, separating the dilute and the dense phase in the grand canonical ensemble. In the mean-field limit we establish contact with queuing theory and show that the kurtosis of the polymer center of mass diverges alike a response function when the system becomes critical, a result which holds for general polymer dynamics (Zimm, Rouse, reptation). Both the equilibrium and nonequilibrium behaviors are solved exactly as a reference study for novel stochastic modeling and experimental setup.

Analysis of the Queuing System for the Indonesian Islamic Bank (BSI) Bengkulu Branch

The purpose of this study is to determine the average level of customer arrivals and the average service time of customers in the queue. The analytical model used in this study is a multi-channel single-phase queuing theory analysis with a mathematical formula. The queuing process is a process related to the arrival of the customer to a queuing system, then waiting in the queue until the waiter selects the customer according to the service discipline, and finally the customer leaves the queuing system after the service is finished. At Bank Syariah Indonesia (BSI) KC Bengkulu S. Parman 1 there are 5 tellers provided to serve customers who will make deposits, withdrawals and cash transfers. Queues that occur at the optimal service level can be obtained by the performance of the queuing system with the calculation results, namely, the average number of customers in the queue (nq) 31.88 customers, customers in the total system 33.08 people, the average time in the queue 0, 000767 and the total system time is 0.034097 or 2 minutes. Thus, customers do not take too long to make transactions. With the number of tellers as many as five people, there is a long waiting time for customers (Wq) in the queue, which is 0.02777 hours or 2 minutes and the average number of customers in the queue (Ls) is 2 people..

Queuing Theory in Traffic Management System

In cities where the number of vehicles has consistently expanded faster than the transportation infrastructure available to serve them. More on queuing theory and its crucial application has been discussed in the current study. In Thudiyalur, Gandhipuram, and Periyanaickenpalayam, all in Coimbatore, this research examines the usefulness of queuing theory in the field of traffic management. The concept of traffic intensity isapplied to a set of areas in queuing theory in this study. Keywords: Traffic intensity, Queuing theory, Single server Poisson model

5G Infrastructure Network Slicing: E2E Mean Delay Model and Effectiveness Assessment to Reduce Downtimes in Industry 4.0

Fifth Generation (5G) is expected to meet stringent performance network requisites of the Industry 4.0. Moreover, its built-in network slicing capabilities allow for the support of the traffic heterogeneity in Industry 4.0 over the same physical network infrastructure. However, 5G network slicing capabilities might not be enough in terms of degree of isolation for many private 5G networks use cases, such as multi-tenancy in Industry 4.0. In this vein, infrastructure network slicing, which refers to the use of dedicated and well isolated resources for each network slice at every network domain, fits the necessities of those use cases. In this article, we evaluate the effectiveness of infrastructure slicing to provide isolation among PLs in an industrial private 5G network. To that end, we develop a queuing theory-based model to estimate the E2E mean packet delay of the infrastructure slices. Then, we use this model to compare the E2E mean delay for two configurations, i.e., dedicated infrastructure slices with segregated resources for each PL against the use of a single shared infrastructure slice to serve the performance-sensitive traffic from PLs. Also we evaluate the use of TSN against bare Ethernet to provide layer 2 connectivity among the 5G system components. We use a complete and realistic setup based on experimental and simulation data of the scenario considered. Our results support the effectiveness of infrastructure slicing to provide isolation in performance among the different slices. Then, using dedicated slices with segregated resources for each PL might reduce the number of the production downtimes and associated costs as the malfunctioning of a PL will not affect the network performance perceived by the performance-sensitive traffic from other PLs. Last, our results show that, besides the improvement in performance, TSN technology truly provides full isolation in the transport network compared to standard Ethernet thanks to traffic prioritization, traffic regulation, and bandwidth reservation capabilities.

The impact of seasonality on efficient airport capacity utilization

The major cause of under-capacity or overcapacity at smaller airports is seasonality. Such airports are finding it difficult to determine the capacity to meet the demand and adequately handle passengers in both high and low season. If the capacity is not optimally defined, excessive congestions and waiting times occur, resulting in lower service quality. Airports greatly benefit from capacity utilization analysis in terms of more accurate planning, designing, and adjusting capacity to the current demand in order to encourage further development as well as to reduce additional costs. Using queuing theory, this paper aims to answer the following question: is the passenger capacity at Rijeka International Airport (Croatia) optimally determined to meet the demand promptly, both in high and low season, without causing excessive congestions and waiting times. The results obtained indicate the occurrence of overcapacity since high season demand can be well served, even with reduced capacity used in the low season when demand is significantly lower.

Workload Control and Order Dispatching Rules

The purpose of this study is to choose an order dispatching rule and measure the work-in-process and lead-time in the production process of a conveyor chain manufacturer. The main strategic issue for the manufacturer is dependability, which requires meeting deadlines and managing internal lead-times. The study integrates two techniques, workload control (WLC) and an analytical hierarchy process (AHP), respectively systems for production planning and control, and multi-criteria decision support, both widely used in handling manufacturing strategic issues. The research method is a field experiment. Supported by the AHP and according to strategic criteria, practitioners selected the early due date rule (the order with the closest due date comes first) to release 231 orders. Then, employing a methodology designed to support WLC applications, the study measured key parameters that provide information regarding the overall performance of the manufacturer, the input rate, work-in-process, lead-time, throughput performance, and the level of safety stock. Using the model and a graphical tool derived from queuing theory, the throughput diagram, the study provides evidence that, although the manufacturing process is satisfactorily balanced and achieves acceptable performance, the level of safety stock is small and should be increased to prevent starvation on the shop floor.

Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.