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Queueing models can be used for making decisions about the resources required to provide high quality service. In this paper, a finite capacity single server queueing model with bulk arrivals is studied in IoT-based edge computing systems. The transient analysis of the model is carried out and the transient analytical solution to the system is derived with a group of recursive coefficients by using the ordinary differential equations (ODEs) technique. From which the steady-state probabilities are solved. Then, some performance metrics of interest are derived along with numerical results. Although the paper is initiated from the IoT based edge computing platform, the proposed system modeling and analysis method can be extended to more general situations such as telecommunication, manufacturing, transportation, and many other areas that are closely related to people’s daily lives.

Queueing models can be used for making decisions about the resources required to provide high quality service. In this paper, a finite capacity single server queueing model with bulk arrivals is studied in IoT-based edge computing systems. The transient analysis of the model is carried out and the transient analytical solution to the system is derived with a group of recursive coefficients by using the ordinary differential equations (ODEs) technique. From which the steady-state probabilities are solved. Then, some performance metrics of interest are derived along with numerical results. Although the paper is initiated from the IoT based edge computing platform, the proposed system modeling and analysis method can be extended to more general situations such as telecommunication, manufacturing, transportation, and many other areas that are closely related to people's daily lives. [ABSTRACT FROM AUTHOR]

This paper studies a single server Markovian queue with the possibility of catastrophes at the service station. In this model, the server takes a maximum number of J vacations till it finds at least one customer in the queue at a vacation completion instant. The time dependent probabilities of the system size are obtained. Four special cases are derived from the model presented in this study. Finally, some numerical computations are presented. [ABSTRACT FROM AUTHOR]

We consider Markovian differentiated hiatuses queues with bulk entries. With the help of the matrix geometric method, we discuss the stability condition for the existence of the steady-state solution of our model and we obtain the stationary system size by using a probability generating function. The stochastic decomposition form of stationary system size and the waiting time distribution of an arbitrary beneficiary are also analysed. Furthermore, we perform the expense analysis using the particle swarm optimization technique and we obtain the optimality of service rate and hiatus rate. Finally, we study the effects of changes in the parameters on some important performance measures of the system through numerical observations. [ABSTRACT FROM AUTHOR]

The authors propose two multirate teletraffic loss models in a two‐link system that accommodates Poisson arriving calls from different service‐classes with different bandwidth‐per‐call requirements. Each link has two thresholds which refer to the number of in‐service calls in the link. The lowest threshold named support threshold, defines up to which point the link can support calls offloaded from the other link. The highest threshold, named offloading threshold, defines the point where the link starts offloading calls to the other link. Two different bandwidth sharing policies are considered: (i) the complete sharing policy, in which a call can be accepted in a link if there exist enough available bandwidth units and (ii) the bandwidth reservation policy, in which an integer number of bandwidth units is reserved to benefit calls of high bandwidth requirements. The two models do not have a product form solution for the steady state probabilities. However, they propose approximate formulas for the calculation of call blocking probabilities. The accuracy of the formulas is verified through simulation and found to be quite satisfactory. [ABSTRACT FROM AUTHOR]

The question of determination of stationary probabilities of the states of the queuing system with an unreliable device, vacation and prophylaxis describing functioning of both basic and auxiliary material stream of the logistic system is considered in the article.В статье рассмотрен вопрос определения стационарных вероятностей состояний системы массового обслуживания с ненадежным прибором, переналадкой и профилактикой, описывающей функционирование как основного, так и вспомогательного материального потока логистической системы.

Drought is a slow and creeping phenomenon that occurs more frequently in arid and semi-arid regions. In recent decades, among natural disasters influencing human societies the number or frequency of drought event has increased more than others. In this context, the prediction of drought intensity, duration and frequency can help to take the necessary precautions and reduce drought risk. This study employs Markov chains of different orders (0, 1, 2 and 3) to analyze hydrological drought characteristics. Hydrological drought is identified based on the streamflow drought index (SDI) at 3-, 6-, 9- and 12-month time scales using data from 21 hydrometric stations located in the Karkheh River Basin in Iran. According to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), first-order Markov chain models are adequate to reproduce the statistical structure of SDI-based hydrological droughts. Moreover, the steady state probabilities and expected residence time of drought severity for all time scales increase as the degree of severity decreases. The results also indicate that the expected frequency of drought occurrence is higher for smaller time scales (i.e., 3-month and 6-month). [ABSTRACT FROM AUTHOR]

A single server general bulk service finite source loss model has been studied. For this model the system steady state probabilities and waiting time distributions are obtained. Some performance measures are also calculated. Particular model is deduced and some numerical examples are also given. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents modeling and analysis of unreliable Markovian multiserver finite-buffer queue with discouragement and synchronous working vacation policy. According to this policy, c servers keep serving the customers until the number of idle servers reaches the threshold level d; then d idle servers take vacation altogether. Out of these d vacationing servers, d W servers may opt for working vacation i.e. they serve the secondary customers with different rates during the vacation period. On the other hand, the remaining d − d W = d V servers continue to be on vacation. During the vacation of d servers, the other e = c − d servers must be present in the system even if they are idle. On returning from vacation, if the queue size does not exceed e, then these d servers take another vacation together; otherwise start serving the customers. The servers may undergo breakdown simultaneously both in regular busy period and working vacation period due to the failure of a main control unit. This main unit is then repaired by the repairman in at most two phases. We obtain the stationary performance measures such as expected queue length, average balking and reneging rate, throughput, etc. The steady state and transient behaviours of the arriving customers and the servers are examined by using matrix analytical method and numerical approach based on Runge–Kutta method of fourth order, respectively. The sensitivity analysis is facilitated for the transient model to demonstrate the validity of the analytical results and to examine the effect of different parameters on various performance indices. [Copyright &y& Elsevier]

A fast and memory efficient recursive method is proposed to calculate the steady state probabilities of M-out-of-N:G reliability model with vacation for repairman. It is assumed that the repair time is exponential, failure time has general distribution and vacation times are independently and identically distributed random variables with general distribution. Using the embedded Markov chain techniques steady state probabilities are computed at pre-arrival epochs and at random epochs. The distribution of waiting time of a unit before the service station (excluding the one with the service facility) has been derived. [ABSTRACT FROM AUTHOR]

A certain Markov chain which was encountered by T. L. Hill in the study of the kinetics of a linear array of enzymes is studied. An explicit formula for the steady state probabilities is given and some conjectures raised by T. L. Hill are proved. [ABSTRACT FROM AUTHOR]

A reduced system is a smaller system derived in the process of analyzing a larger system. In solving for steady state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability (or rate) matrix. Following Lal (1981), a Markov chain can be categorized as standard or nonstandard depending on the location of an invertible submatrix necessary for an efficient solution in a transition probability (or rate) matrix. In this paper, algorithms for the determination of steady state probabilities are developed by using (i) a backward recursion which is efficient for standard systems and (ii) a forward recursion which is efficient for nonstandard systems. It is also shown that the backward recursion can be used for finding the first passage time distribution and its mean and variance. [ABSTRACT FROM AUTHOR]

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