Negative Arrivals Research Articles

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

The maximum entropy principle has grown progressively more pertinent to queueing systems. The principle of maximum entropy (PME) presents an impartial framework as a promising method to examine complex queuing processes. This principle can be employed to assess the most appropriate probability distributions for queueing scenarios in a variety of widespread industrial issues. The aspects of general service bulk arrival retrial G-queue including working vacation, state-dependent arrival, priority users, and working breakdown are all explored in this article. Real-world applications for this kind of waiting line include computer systems, industrial companies, packet-switching networks, and communication facilities, etc. The adverse users (or negative arrivals) can make an appearance when the server (operator) is preoccupied with a positive user. Consumer’s arrival patterns follow the Poisson distribution. Priority consumers and regular (ordinary) consumers are the two groups of consumers that are considered in this investigation. Priority consumers do not have to wait in line and are granted a special right of prevention that allows them to receive services before ordinary consumers. Initially, we have estimated performance metrics including orbit size and long-run probabilities in this research work. The maximum entropy approach is then used to give a comparative perusal between the system’s exact and estimated waiting times. Apart from that a bi-objective optimization model is developed to diminish both consumers waiting times and estimated costs simultaneously. It is manageable to establish an effective balance between the standard of service and operating expenses using the analytical strategy that has been provided.

Investigation on inventory replenishment policy for a queueing system with catastrophic failure, negative arrival and discouraged customers

Investigation on inventory replenishment policy for a queueing system with catastrophic failure, negative arrival and discouraged customers

Analysis of Non-Markovian batch arrival retrial queue with priority services, Vacation and Vacation Interruption Under Random Environment, Negative Arrival, Immediate Feedback, Differentiate Breakdown, Repair

Analysis of Non-Markovian batch arrival retrial queue with priority services, Vacation and Vacation Interruption Under Random Environment, Negative Arrival, Immediate Feedback, Differentiate Breakdown, Repair

Reliability and Optimum Cost Analysis of Malware Infected System by Discrete-Time Negative Arrival Retrial Queue

The failure of computer software system is inevitable and it is important to analyze the performance of the system. It is equally important to consider the cost factor that occurs during repair. This paper models malware infected system and analyzes its behavior using a hybrid technique. A likelihood estimation is used for filtering malwares and improving the performance of the system. A discrete-time single server retrial queue with two types of arrivals is modeled to address infected system characteristics. A request which is originally legitimate known as the positive arrival, who finds the host free gets instant service; otherwise it joins the buffer. The malware (request) which is not detected by the filter known as the negative arrival will lead to the breakdown of the server, irrespective of the fact that the server is idle or busy. Further, it is assumed that suspicious request has no impact on the system when the server is under repair. Once the server is affected by suspicious request, it is sent for repair immediately. The retrial, service, and repair times are arbitrarily distributed. Performance characteristics such as mean buffer size, mean waiting time have been obtained. The reliability measures such as server availability, failure frequency, probability of packet lost, reliability of the underlying queueing system have also been derived. A cost model has been developed. The efficacy of filtering method and its level of accuracy have been demonstrated experimentally. The infected system has been detected from the performance measures and reliability metrics. A comparative study with and without filtering has been discussed numerically. The optimum cost analysis has also been presented.

Computational Approach for Transient Behaviour of Finite Source Retrial Queueing Model with Multiple Vacations and Negative Arrival

We are analyzing a transient behavior of finite source retrial model with multiple vacations and negative arrival in which the primary arrival rate λ, a Poisson, service time μ, α an exp. distribution. We have assumed that the finite calling population size Fs α obeys an exponential distribution for vacation rate. All transitions are assembled by using an infinitesimal generator matrix (IGM). Cayley Hamilton Method is used to obtain the time dependent and steady state solutions. Computational studies done for analysis of time dependent solutions of mean no. of occupants in the orbit and prob. of server free/busy/vacation for all Fs , λ, μ, α, δ, σ, and t.

Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations

We study the economic analysis of a single server Markovian queueing system with positive and negative customers and multiple working vacations. Both positive and negative customers arrive in the system according to a Poisson process. Upon arrival, positive customers acquire some system information and decide whether to join or to balk the system based on the acquired information and a linear cost-reward structure. Negative customers on arrival break the server and kill the positive customer in service. The server is immediately sent for repair, and no customers are allowed during a repair. The server takes multiple working vacations after serving all the positive waiting customers. We obtain the equilibrium strategies and social benefit of positive customers under four different information situations. Numerical experiments are presented to show the effects of model parameters and information levels on the equilibrium joining behavior of positive customers.

Sp Receiver-Function Images of African and Arabian Lithosphere: Survey of Newly Available Broadband Data

Abstract The growing quality and improving spatial coverage of broadband seismic stations on the African (Nubian + Somalian) and Arabian plates motivate us to present a catalog of S-to-P receiver functions (SRFs) from southern Africa to northern Arabia. As in North America where the ability to compare data from cratons to modern rift provinces has led to new insights about lithospheric discontinuities, so, too, in Africa and Arabia can we begin to track and study the Moho, midlithospheric discontinuities, and the lithosphere–asthenosphere boundary (LAB) between tectonothermal provinces and beneath plate boundaries. We utilized 1508 seismic stations recording 9349 teleseismic events to calculate 103,878 SRFs that we stacked in 1° circular bins. We find a robust positive arrival due to a seismic-wavespeed increase downward across the Moho in virtually all our stacked SRF traces at 15–55 km depth, and we verify this is in good agreement with previously published Ps results, thereby validating the quality of our data set. Our stacked SRF traces also show a sub-Moho negative arrival at a delay time equivalent to 50–132 km depth that should correspond to a negative velocity discontinuity at or above the LAB. Our continent-wide, plate-scale database offers the opportunity to explore for spatial and temporal evolution of lithospheric parameters.

Unified killing mechanism in a single server queue with renewal input

Queueing systems experienced in real-life situations are very often influenced by negative arrivals which are independent of service process and cause the elimination of jobs from the system. Such a scenario occurs in computer network and telecommunication systems where an attack by a malicious virus results in the removal of some or all data files from the system. Along this direction many authors have proposed various killing processes in the past. This paper unifies different killing mechanisms into the classical single server queue having infinite capacity, where arrival occurs as renewal process with exponential service time distribution. The system is assumed to be affected by negative customers as well as disasters. The model is investigated in steady-state in a very simple and elegant way by means of supplementary variable and difference equation technique. The distribution of system-content for the positive customers is derived in an explicit form at pre-arrival and random epochs. The influence of different parameters on the system performance are also examined.

Stationary queue length distribution of a continuous-time queueing system with negative arrival

This paper studies a continuous-time single-server infinite capacity queueing system with two types of customer: positive and negative customers. Positive customers are ordinary customers that receives service in the server. A negative customer that arrives to the system according to a Poisson process with rate γ will remove one positive customer at the head upon its arrival. By assuming that the interarrival time and service time distributions tend to a constant when time t goes to infinity, a set of equations will be derived by using an alternative approach to find the stationary queue length distribution. Numerical results obtained by the alternative approach will be compared to those obtained by the existing method and verified by the simulation procedure.

Lithospheric layering beneath the contiguous United States constrained by S-to-P receiver functions

To image upper mantle seismic discontinuities beneath the contiguous United States, a total of 284,121 S-to-P receiver functions (SRFs) recorded by 3,594 broadband seismic stations in the EarthScope Transportable Array and other permanent and temporary deployments are stacked in circular bins of 2° in radius. A robust negative arrival, representing a sharp discontinuity of wave speed reduction with depth, is visible in virtually all the stacked traces in the depth range of 30–110 km. Beneath the western U.S., the mean depth of this discontinuity is 69±17 km, and beneath the eastern U.S., it is 76±5 km, both are comparable to the depth of the tomographically-determined lithosphere–asthenosphere boundary (LAB). In contrast, the depth of the discontinuity beneath the stable cratonic region of the central U.S. is 87±6 km, which is significantly shallower than the ∼250 km LAB depth determined by seismic tomography. Based on the amplitude of the corresponding arrival in the SRFs and findings from previous seismic tomography and mantle xenolith studies, this discontinuity beneath the central U.S. is interpreted as the top of an intra-lithospheric low wave speed, probably phlogopite-rich layer. The observations provide new constraints on a number of regional scale tectonic processes, such as lithospheric stretching in the Texas–Louisiana Gulf Coastal Plain and the Basin and Range Province, and possible lithospheric basal erosion beneath the northeastern U.S.

Transient Analysis of $$M^{[X_{1}]},M^{[X_{2}]}/G_{1},G_{2}/1$$ M [ X 1 ] , M [ X 2 ] / G 1 , G 2 / 1 Retrial Queueing System with Priority Services, Working Vacations and Vacation Interruption, Emergency Vacation, Negative Arrival and Delayed Repair

This paper deals with the analysis of two classes of batch arrivals, one is high priority and other is low priority(retrial) customers with non-preemptive priority service, working vacations, negative arrival, emergency vacation for an unreliable server, which consists of a break-down by negative arrival and delay time to start repair. When there are no customers in the queue and in the orbit at the time of service completion for a positive customers, the server goes for a working vacation. The server works at a lower service rate during working vacation period. If there are no customers in the system at the end of vacation, the server becomes idle and ready for serving the new arrivals with probability p(single working vacation) or it remains on vacation with probability $$q=(1{-}p)$$ (multiple working vacations). Here we assume that customers arrive according to compound Poisson process in which high priority customers are assigned to class one and class two customers are of a low priority type. The priority customers that find the server busy are queued and then served in accordance with FCFS discipline. The arriving low priority customers on finding the server busy are queued in the orbit in accordance with FCFS constant retrial policy. The arrival of negative customer remove the customer being in service and makes the server breakdown and the server fail for a short interval of time. When the server fails it will send to repair. But the repair time do not start immediately, there is a delay time to start the repair process. We consider an emergency vacation which means that during the service time the server suddenly go for a vacation and the interrupted customer waits to getting the remaining service. The retrial time, service time, emergency vacation time, delay time and repair time are all follows general(arbitrary) distribution, working vacation time and negative arrival follows exponential distribution. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained explicitly. Also some performance measures of our model such as the system state probabilities, reliability indices, the average number of customer in the high priority queue and the low priority in the orbit and the average waiting time are derived. Numerical results are computed and graphical representations are presented.

Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions

In this paper, a single-server queue with negative customers is considered. The arrival of a negative customer will remove one positive customer that is being served, if any is present. An alternative approach will be introduced to derive a set of equations which will be solved to obtain the stationary queue length distribution. We assume that the service time distribution tends to a constant asymptotic rate when time t goes to infinity. This assumption will allow for finding the stationary queue length of queueing systems with non-exponential service time distributions. Numerical examples for gamma distributed service time with fractional value of shape parameter will be presented in which the steady-state distribution of queue length with such service time distributions may not be easily computed by most of the existing analytical methods.

On the multiserver retrial queues with negative arrivals.

The paper deals with an M/M/C/K retrial queue with exponential abandonment at which positive and negative customers arrive according to Poisson processes. This model is of practical interest: it can be used for analysing the performance in call centres and e-mail contact systems. For the model under investigation, we find the ergodicity conditions and also the approximate solution by using finite truncation and value extrapolation methods. We present some numerical results to examine the performance of the value extrapolation method as well as the system performance.

On the multiserver retrial queues with negative arrivals

On the multiserver retrial queues with negative arrivals

Modeling the Internet of Things Under Attack: A G-network Approach

This paper introduces a novel, analytic framework for modeling security attacks in Internet of Things (IoT) infrastructures. The devised model is quite generic, and as such, it could flexibly be adapted to various IoT architectures. Its flexibility lies in the underlying theory; it is based on a dynamic G-network, where the positive arrivals denote the data streams that originated from the various data collection networks (e.g., sensor networks), while the negative arrivals denote the security attacks that result in data losses (e.g., jamming attacks). In addition, we take into account the intensity of an attack by considering both light and heavy attacks. The light attack implies simple losses of traffic data, while the heavy attack causes massive data loss. The introduced model is solved subject to the arrival and departure rates in terms of: 1) average number of data packets in the application domain and 2) attack impact (loss rate). A comprehensive verification discussion accompanied by numerous numerical results verify the accuracy of the proposed model. Moreover, the assessment of the presented model highlights notable operation characteristics of the underlying IoT system under light and heavy attacks.

Lithospheric discontinuities beneath the U.S. Midcontinent – signatures of Proterozoic terrane accretion and failed rifting

Seismic discontinuities between the Moho and the inferred lithosphere–asthenosphere boundary (LAB) are known as mid-lithospheric discontinuities (MLDs) and have been ascribed to a variety of phenomena that are critical to understanding lithospheric growth and evolution. In this study, we used S-to-P converted waves recorded by the USArray Transportable Array and the OIINK (Ozarks–Illinois–Indiana–Kentucky) Flexible Array to investigate lithospheric structure beneath the central U.S. This region, a portion of North America's cratonic platform, provides an opportunity to explore how terrane accretion, cratonization, and subsequent rifting may have influenced lithospheric structure. The 3D common conversion point (CCP) volume produced by stacking back-projected Sp receiver functions reveals a general absence of negative converted phases at the depths of the LAB across much of the central U.S. This observation suggests a gradual velocity decrease between the lithosphere and asthenosphere. Within the lithosphere, the CCP stacks display negative arrivals at depths between 65 km and 125 km. We interpret these as MLDs resulting from the top of a layer of crystallized melts (sill-like igneous intrusions) or otherwise chemically modified lithosphere that is enriched in water and/or hydrous minerals. Chemical modification in this manner would cause a weak layer in the lithosphere that marks the MLDs. The depth and amplitude of negative MLD phases vary significantly both within and between the physiographic provinces of the midcontinent. Double, or overlapping, MLDs can be seen along Precambrian terrane boundaries and appear to result from stacked or imbricated lithospheric blocks. A prominent negative Sp phase can be clearly identified at 80 km depth within the Reelfoot Rift. This arrival aligns with the top of a zone of low shear-wave velocities, which suggests that it marks an unusually shallow seismic LAB for the midcontinent. This boundary would correspond to the top of a region of mechanically and chemically rejuvenated mantle that was likely emplaced during late Precambrian/early Cambrian rifting. These observations suggest that the lithospheric structure beneath the Reelfoot Rift may be an example of a global phenomenon in which MLDs act as weak zones that facilitate the removal of cratonic lithosphere that lies beneath.

Transient Solution of M[x1],M[x2]/G1,G2/1 Retrial queueing system with Priority services, Modified Bernoulli Vacation, Bernoulli Feedback, Negative arrival, Breakdown, Delaying repair, Setup time and Balking

Transient Solution of M[x1],M[x2]/G1,G2/1 Retrial queueing system with Priority services, Modified Bernoulli Vacation, Bernoulli Feedback, Negative arrival, Breakdown, Delaying repair, Setup time and Balking

Queue Length and Busy Period Analysis for the M/G/1 Queue with Negative Arrivals

In this paper, the queue lengths and the busy period lengths of the M/G/1 queueing systems with negative arrivals are analyzed. Two types of negative arrivals are considered. One type is negative customers and the other type is disasters. When a negative customer arrives to a system, one positive customer is removed if the number of positive customers is more than one. In particular, we assume the RCH (Removal of a Customer at the Head) type of negative customers which represent a kind of work-canceling signal to the positive customer in service. On the other hand, disasters get rid of all customers in the system. In this paper, the Probability Generating Function (PGF) of the stationary queue length and busy period length of M/G/1 queue with both negative customers and disasters are derived.

M/M/1 Retrial queueing system with negative arrival under non-preemptive priority service

Consider a single server retrial queueing system with negative arrival under non-pre-emptive priority service in which three types of customers arrive in a poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers and λ3 for negative arrival. Low and high priority customers are identified as primary calls. The service times follow an exponential distribution with parameters μ1 and μ2 for low and high priority customers. The retrial and negative arrivals are introduced for low priority customers only. Gelenbe (1991) has introduced a new class of queueing processes in which customers are either positive or negative. Positive means a regular customer who is treated in the usual way by a server. Negative customers have the effect of deleting some customer in the queue. In the simplest version, a negative arrival removes an ordinary positive customer or a random batch of positive customers according to some strategy. It is noted that the existence of a flow of negative arrivals provides a control mechanismto control excessive congestion at the retrial group and also assume that the negative customers only act when the server is busy. Let K be the maximumnumber of waiting spaces for high priority customers in front of the service station. The high priorities customers will be governed by the Non-preemptive priority service. The access from the orbit to the service facility is governed by the classical retrial policy. This model is solved by using Matrix geometric Technique. Numerical study have been done for Analysis of Mean number of low priority customers in the orbit (MNCO), Mean number of high priority customers in the queue(MPQL),Truncation level (OCUT),Probability of server free and Probabilities of server busy with low and high priority customers for various values of λ1 , λ2 , λ3 , μ1 , μ2 ,σ and k in elaborate manner and also various particular cases of this model have been discussed.

Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers

This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using embedded Markov chain technique and the supplementary variable method, we present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state. The waiting process is also given. Some main reliability measures, such as the availability, failure frequency, and the reliability function of the server, are obtained. Finally, some numerical examples and cost optimization analysis are presented.