Interarrival Times Research Articles

Covert Timing Channel Analysis Either as Cyber Attacks or Confidential Applications.

Covert timing channels are an important alternative for transmitting information in the world of the Internet of Things (IoT). In covert timing channels data are encoded in inter-arrival times between consecutive packets based on modifying the transmission time of legitimate traffic. Typically, the modification of time takes place by delaying the transmitted packets on the sender side. A key aspect in covert timing channels is to find the threshold of packet delay that can accurately distinguish covert traffic from legitimate traffic. Based on that we can assess the level of dangerous of security threats or the quality of transferred sensitive information secretly. In this paper, we study the inter-arrival time behavior of covert timing channels in two different network configurations based on statistical metrics, in addition we investigate the packet delaying threshold value. Our experiments show that the threshold is approximately equal to or greater than double the mean of legitimate inter-arrival times. In this case covert timing channels become detectable as strong anomalies.

Cost and revenue analysis of an impatient customer queue with second optional service and working vacations

In this article, we propose a finite buffer impatient customer queue with second optional service (SOS) and working vacations. When the server is busy, an arriving customer either joins the queue or balks on the basis of state-dependent joining/balking probabilities. For each customer, the server provides two phases of service, namely, first essential service (FES) and SOS. All the customers demand FES, whereas only few customers opt for SOS after the completion of FES. At a service completion instant, if the system is empty, the server leaves for working vacation. During working vacations, the waiting customers activate an impatient timer which is exponentially distributed. It is assumed that the interarrival times, vacation times, service times during FES, SOS and during working vacations follow exponential distribution. The steady-state probabilities of the model and various performance measures are derived. In order to optimize the total expected cost of the system, particle swarm optimization technique has been adopted for finding the optimum service rates of the server. Numerical results are sketched out to demonstrate the impact of the system and cost parameters.

A Variational Point Process Model for Social Event Sequences

Many events occur in real-world and social networks. Events are related to the past and there are patterns in the evolution of event sequences. Understanding the patterns can help us better predict the type and arriving time of the next event. In the literature, both feature-based approaches and generative approaches are utilized to model the event sequence. Feature-based approaches extract a variety of features, and train a regression or classification model to make a prediction. Yet, their performance is dependent on the experience-based feature exaction. Generative approaches usually assume the evolution of events follow a stochastic point process (e.g., Poisson process or its complexer variants). However, the true distribution of events is never known and the performance depends on the design of stochastic process in practice. To solve the above challenges, in this paper, we present a novel probabilistic generative model for event sequences. The model is termed Variational Event Point Process (VEPP). Our model introduces variational auto-encoder to event sequence modeling that can better use the latent information and capture the distribution over inter-arrival time and types of event sequences. Experiments on real-world datasets prove effectiveness of our proposed model.

Software-Based Validation of the Differentiation Scheme for Ethernet and Wireless LAN Access Network Types Using an End-to-End Approach

Different access network types are characterized by a variety of attributes which include link bandwidths, physical media, capacity, and reliability. Therefore, the question of accurately identifying whether the sender uses a wired ethernet connection or a wireless LAN connection comes into place. This article aims to analyse, simulate, validate, and improve the existing classification scheme which is based on measuring entropy of packet pair inter-arrival times and median. A riverbed modeller (former OPNET) is used for simulating the different scenarios. Small-scale experiment conducted on campus at the Nazarbayev University (NU) validates the insignificance of the packet probe size chosen for the classification.

Performance evaluation of a carousel configured multiple products flexible manufacturing system using Petri net

This study presents a schematic approach to model, simulate and analyze the overall performance of an FMS, comprising a carousel layout surrounded by manufacturing and assembly cells capable to deliver a variety of multiple products. All manufacturing and assembly cells are consisting of multiple multifunctional production and assembly machines, served by material loading and unloading robots, connected through a material transporting conveyor. Inter-cellular and intra-cellular routing flexibility are employed in the system through production resources operational and breakdown modes. Colored Petri net tools are used to develop a compact, editable and deadlock-free flexible manufacturing system model reveals important information about dynamic behavior and system performance measures e.g.; throughput, mean cycle time, and work-in-process (WIP) with reference to material handling and supply system, production resources reliability and process execution input variables. Variation in input factors namely mean machining and assembly time, material loading and unloading time, number of operations between failure, repair time, parts inter-arrival time, conveyor speed and buffer capacity have shown a substantial effect on the system performance. The results indicate successful applicability of colored Petri net tools for modelling, simulation, and evaluation of carousel configured multiple products flexible manufacturing system. Further, the optimal solution represents a deep relationship between the different production modes and responses to maximize the performance of a carousel configured multiple products FMS.

On the coherent systems subject to Marshall-Olkin type shocks

Coherent systems and Marshall-Olkin run shock models are combined. Coherent systems consisting of n components receive some kind of shocks from n+1 different sources similar to Marshall-Olkin type. More precisely, when the component j receives k consecutive fatal shocks from the source j or k consecutive fatal shocks from the source n+1, it fails, j = 1, …,n. When the interarrival time of shocks has phase-type distribution, reliability, mean time to failure (MTTF) and mean residual life (MRL) function of the coherent systems are studied. Numerical examples and graphical representations are provided.

Uncertain insurance risk process with multiple classes of claims

Traditionally, an insurance risk process describes an insurance company’s risk through some criteria using the historical data under the framework of probability theory with the prerequisite that the estimated distribution function is close enough to the true frequency. However, because of the complexity and changeability of the world, economical and technological reasons in many cases enough historical data are unavailable and we have to base on belief degrees given by some domain experts, which motivates us to include the human uncertainty in the insurance risk process by regarding interarrival times and claim amounts as uncertain variables using uncertainty theory. Noting the expansion of insurance companies’ operation scale and the increase of businesses with different risk nature, in this paper we extend the uncertain insurance risk process with a single class of claims to that with multiple classes of claims, and derive expressions for the ruin index and the uncertainty distribution of ruin time respectively. As the ruin time can be infinite, we propose a proper uncertain variable and the corresponding proper uncertainty distribution of that. Some numerical examples are documented to illustrate our results. Finally our method is applied to a real-world problem with some satellite insurance data provided by global insurance brokerage MARSH.

ON TIME-TO-BUFFER OVERFLOW DISTRIBUTION IN A SINGLE-MACHINE DISCRETE-TIME SYSTEM WITH FINITE CAPACITY

A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well.

Recession analysis revisited: impacts of climate on parameter estimation

Abstract. Recession analysis is a classical method in hydrology to assess watersheds' hydrological properties by means of the receding limb of a hydrograph, frequently expressed as the rate of change in discharge (-dQ/dt) against discharge (Q). This relationship is often assumed to take the form of a power law -dQ/dt=aQb, where a and b are recession parameters. Recent studies have highlighted major differences in the estimation of the recession parameters depending on the method, casting doubt on our ability to properly evaluate and compare hydrological properties across watersheds based on recession analysis of -dQ/dt vs. Q. This study shows that estimation based on collective recessions as an average watershed response is strongly affected by the distributions of event inter-arrival time, magnitudes, and antecedent conditions, implying that the resulting recession parameters do not represent watershed properties as much as they represent the climate. The main outcome from this work highlights that proper evaluation of watershed properties is only ensured by considering independent individual recession events. While average properties can be assessed by considering the average (or median) values of a and b, their variabilities provide critical insight into the sensitivity of a watershed to the initial conditions involved prior to each recharge event.

Optimizing Throughput, WIP and Cycle Time: A Case Study of Utensils Manufacturing Shop Floor

The development of simulation models for improving performances is trendy in manufacturing industries. This paper presents simulation model for evaluating and improving performances of a utensils manufacturing plant. Internal benchmarking is employed for comparison under exactly similar conditions. The data of all input variables is collected and statistical models for each process is developed using Arena input analyzer. The simulation model is then developed using SIMIO to optimize throughput, work-in-process, and cycle time. The experiments have been performed under various scenarios i.e. at different values of the input parameters. The areas for improvement have been highlighted on the basis of results. Furthermore, best and worst case scenarios have been discussed in detail to provide insights for managerial performance improvements by: (1) optimizing inter-arrival time, (2) increasing production rate, and (3) reducing the number of rejected parts without disturbing existing set up of the manufacturing facility.

A bound on the rate of convergence in the central limit theorem for renewal processes under second moment conditions

AbstractA famous result in renewal theory is the central limit theorem for renewal processes. Since, in applications, usually only observations from a finite time interval are available, a bound on the Kolmogorov distance to the normal distribution is desirable. We provide an explicit non-uniform bound for the renewal central limit theorem based on Stein’s method and track the explicit values of the constants. For this bound the inter-arrival time distribution is required to have only a second moment. As an intermediate result of independent interest we obtain explicit bounds in a non-central Berry–Esseen theorem under second moment conditions.

On the ratio of current age to total life for null recurrent renewal processes

A number of open problems associated with determining the limit distribution of the ratio of current age to total life for a null recurrent renewal process (i.e. where inter-arrival times have infinite mean) are solved. In particular, when the survival function for the inter-arrival times satisfies F̄(t)∼t−αL(t) as t→∞ with L slowly varying and 0≤α≤1, we prove that the limit distribution corresponds to that of U1∕α, where U is uniformly distributed on (0,1), with the limit distribution taken to be degenerate at 0 when α=0. By using direct methods instead of appealing to strong renewal theorems, we are able to prove this result without regard to whether the inter-arrival time distribution is latticed or not, and without extraneous constraints on the renewal function.

Survey-based calibration of a parking entry as a single-server mathematical queuing model: A case study

Traffic congestion is observed around shopping malls, mostly, due to the long queue at the parking entry gates. The queuing theory is an operation research technique that mathematically models the queuing systems consisting of randomly arriving costumers to receive service and then depart such as the parking entry gates. For a single-server mathematical queuing model, the inter-arrival time is usually assumed to be negative exponentially distributed (Poisson process). Mostly, the service times are assumed to be either similar to inter-arrival, M/M/1, or constant, M/D/1; neither assumptions is correct in terms of producing performance measures that conform with the reality. However, the M/D/1 model seems to perform more closely. This paper proposes an approach to apply the mathematical queuing model for such system more efficiently. Essentially, service time is calibrated to the best fitting distribution based on the data collected from major shopping malls in Alexandria and Giza in 2016 and 2017; respectively. The calibration proves that the service time is normally distributed. The application of the M/D/1 using the mean time of the calibrated normal distribution as the constant service time is then tested. The resulted performance measures show a significant conformity with the performance measures of the field data.

Algorithms for the upper bound mean waiting time in the GI/GI/1 queue

It has long been conjectured that the tight upper bound for the mean steady-state waiting time in the GI/GI/1 queue given the first two moments of the interarrival-time and service-time distributions is attained asymptotically by two-point distributions. The two-point distribution for the interarrival time has one mass point at 0, but the service-time distribution involves a limit; there is one mass point at a high value, but that upper mass point must increase to infinity while the probability on that point must decrease to 0 appropriately. In this paper, we develop effective numerical and simulation algorithms to compute the value of this conjectured tight bound. The algorithms are aided by reductions of the special queues with extremal interarrival-time and extremal service-time distributions to D/GI/1 and GI/D/1 models. Combining these reductions yields an overall representation in terms of a D/RS(D)/1 discrete-time model involving a geometric random sum of deterministic random variables (the RS(D)), where the two deterministic random variables in the model may have different values, so that the extremal steady-state waiting time need not have a lattice distribution. Efficient computational methods are developed. The computational results show that the conjectured tight upper bound offers a significant improvement over established bounds.

Optimal control of production-inventory systems with correlated demand inter-arrival and processing times

We consider the production control problem of a production-inventory system with correlated demand inter-arrival and processing times that are modeled as Markovian Arrival Processes. The control problem is minimizing the expected average cost of the system in the steady-state by controlling when to produce an available part. We prove that the optimal control policy is the state-dependent threshold policy. We evaluate the performance of the system controlled by the state-dependent threshold policy by using the Matrix Geometric method. We determine the optimal threshold levels of the system by using policy iteration. We then investigate how the autocorrelation of the arrival and service processes impact the performance of the system. Finally, we compare the performance of the optimal policy with 3 benchmark policies: a state-dependent policy that uses the distribution of the inter-event times but assumes i.i.d.inter-event times, a single-threshold policy that uses both the distribution and also the autocorrelation, and a single-threshold policy that uses the distribution of the inter-event times but assumes they are not correlated. Our analysis demonstrates that ignoring autocorrelation in setting the parameters of the production policy causes significant errors in the expected inventory and backlog costs. A single-threshold policy that sets the threshold based on the distribution and also the autocorrelation performs satisfactorily for systems with negative autocorrelation. However, ignoring positive correlation yields high errors for the total cost. Our study shows that an effective production control policy must take correlations in service and demand processes into account.

A note on the uniform asymptotic behavior of the finite-time ruin probability in a nonstandard renewal risk model

Consider a nonstandard renewal risk model in which claims and interarrival times form a sequence of independent and identically distributed random pairs, with each pair obeying arbitrary dependence or size-dependence structure. In the case of heavy-tailed claims, we obtain the asymptotic behavior of finite-time ruin probability with the uniformity in time in some infinite regions.

Markovian Model of Unreliable Server Retrial Queue with Discouragement

In this paper, we present the performance analysis of Markovian retrial queue with unreliable server by incorporating the features of balking and reneging. The customers may abandon the queue at the moment of busy server or at the departure epoch from the orbit zone. When the customers notice the server in busy state, they will join to the orbit zone and wait there to avail the service. After a random period, the customers from the orbit either may try for the re-attempts for the service or may renege from the system without getting the service. Markov model is developed by considering the inter-arrival, retrial and service times governed by the exponential distributions. The probabilities of the system states are determined by implementing recursive approach to solve the governing Chapman–Kolmogorov equations. The cost function is constructed which is further used to find the total expected cost and associated optimal service rate of the system. A numerical illustration is provided to explore the system metrics with respect to various system descriptors.

Estimates for the Finite-Time Ruin Probability of a Time-Dependent Risk Model with a Brownian Perturbation

In this paper, we consider a time-dependent risk model with a Brownian perturbation. In this model, there is a dependence structure between the claim sizes and their corresponding interarrival times. Assuming the claim sizes have subexponential distributions, we obtain the asymptotic lower bound of the finite-time ruin probability. When the claim sizes have distributions from the class L∩D, the asymptotic upper bound of the finite-time ruin probability has been presented. These results confirm that when the claim sizes are heavy-tailed, the asymptotics of the finite-time ruin probability of this time-dependent model are insensitive to the Brownian perturbation.

Analysis of the infinite server queues with semi-Markovian multivariate discounted inputs

We consider a general k-dimensional discounted infinite server queueing process (alternatively, an incurred but not reported claim process) where the multivariate inputs (claims) are given by a k-dimensional finite-state Markov chain and the arrivals follow a renewal process. After deriving a multidimensional integral equation for the moment-generating function jointly to the state of the input at time t given the initial state of the input at time 0, asymptotic results for the first and second (matrix) moments of the process are provided. In particular, when the interarrival or service times are exponentially distributed, transient expressions for the first two moments are obtained. Also, the moment-generating function for the process with deterministic interarrival times is considered to provide more explicit expressions. Finally, we demonstrate the potential of the present model by showing how it allows us to study semi-Markovian modulated infinite server queues where the customers (claims) arrival and service (reporting delay) times depend on the state of the process immediately before and at the switching times.

The finite-time ruin probability of time-dependent risk model with stochastic return and Brownian perturbation

This paper considers a dependent risk model with stochastic return and Brownian perturbation, where there exists a dependence structure between the claim sizes and the inter-arrival times and the price process of the investment portfolio is a geometric Levy process. When the claim sizes have heavy-tailed distributions, the asymptotic lower and upper bounds of the finite-time ruin probability have been given.