Search

The article presents the results of a study on modeling cloud systems. In this research, the authors developed both analytical and simulation models. System analysis was conducted at the level of virtual machine support, corresponding to Infrastructure as a Service (IaaS). The models assumed that virtual machines of different sizes are offered as part of IaaS, reflecting the heterogeneous nature of modern systems. Additionally, it was assumed that due to limitations in access to physical server resources, only a portion of these resources could be used to create virtual machines. The model is based on Markov chain analysis for state-dependent systems. The system was divided into an external structure, represented by a collection of physical machines, and an internal structure, represented by a single physical machine. The authors developed a novel approach to determine the equivalent traffic, approximating the real traffic appearing at the input of a single physical machine under the assumptions of request distribution. As a result, it was possible to determine the actual request loss probability in the entire system. The results obtained from both models (simulation and analytical) were summarized in common graphs. The studies were related to the actual parameters of commercially offered physical and virtual machines. The conducted research confirmed the high accuracy of the analytical model and its independence from the number of different instances of virtual machines and the number of physical machines. Thus, the model can be used to dimension cloud systems. [ABSTRACT FROM AUTHOR]

This paper uses a bottom-up, reduced form credit risk model with hazard rate estimated default probabilities to compute various collateralised loan obligation (CLO) tranches' loss probabilities and capital factors. It is shown that with respect to the loss probabilities, credit rated CLO tranches are less risky than comparably rated corporate bonds. In addition, a similar argument can be made that corporate debt loss rates will be on average larger than equally rated CLO tranche loss rates. And, it is shown that the National Association of Insurance Commissioners (NAIC) capital factors are typically larger than value-at-risk based capital factors. The policy implication is that NAIC capital factors distort investment incentives by requiring too much capital for CLOs relative to equally rated corporate debt. [ABSTRACT FROM AUTHOR]

In many stochastic problems, the output of interest depends on an input random vector mainly through a single random variable (or index) via an appropriate univariate transformation of the input. We exploit this feature by proposing an importance sampling method that makes rare events more likely by changing the distribution of the chosen index. Further variance reduction is guaranteed by combining this single-index importance sampling approach with stratified sampling. The dimension-reduction effect of single-index importance sampling also enhances the effectiveness of quasi-Monte Carlo methods. The proposed method applies to a wide range of financial or risk management problems. We demonstrate its efficiency for estimating large loss probabilities of a credit portfolio under a normal and t-copula model and show that our method outperforms the current standard for these problems. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples.

In this paper, we analyze a multi-server queueing system with heterogeneous customers that arrive according to a marked Markovian arrival process. Customers of two types differ in priorities and parameters of phase type distribution of their service time. The queue under consideration can be used to model the processes of information transmission in telecommunication networks in which often the flow of information is the superposition of several types of flows with correlation of inter-arrival times within each flow and cross-correlation. We define the process of information transmission as the multi-dimensional Markov chain, derive the generator of this chain and compute its stationary distribution. Expressions for computation of various performance measures of the system, including the probabilities of loss of customers of different types, are presented. Output flow from the system is characterized. The presented numerical results confirm the high importance of account of correlation in the arrival process. The values of important performance measures for the systems with the correlated arrival process are essentially different from the corresponding values for the systems with the stationary Poisson arrival process. Measurements in many real world systems show poor approximation of real flows by such an arrival process. However, this process is still popular among the telecommunication engineers due to the evident existing gap between the needs of adequately modeling the real life systems and the current state of the theory of algorithmic methods of queueing theory.

This paper seeks to identify computationally efficient importance sampling (IS) algorithms for estimating large deviation probabilities for the loss on a portfolio of loans. Related literature typically assumes that realised losses on defaulted loans can be predicted with certainty, i.e., that loss given default (LGD) is non-random. In practice, however, LGD is impossible to predict and tends to be positively correlated with the default rate and the latter phenomenon is typically referred to as PD-LGD correlation (here PD refers to probability of default, which is often used synonymously with default rate). There is a large literature on modelling stochastic LGD and PD-LGD correlation, but there is a dearth of literature on using importance sampling to estimate large deviation probabilities in those models. Numerical evidence indicates that the proposed algorithms are extremely effective at reducing the computational burden associated with obtaining accurate estimates of large deviation probabilities across a wide variety of PD-LGD correlation models that have been proposed in the literature.

In this paper, we consider a general state-dependent finite-buffer bulk queue in which the rates and batch sizes of arrivals and services are allowed to depend on the number of customers in queue and service batch sizes. Such queueing systems have rich applications in manufacturing, service operations, computer and telecommunication systems. Interesting examples include batch oven processes in the aircraft and semiconductor industry; serving of passengers by elevators, shuttle buses, and ferries; and congestion control mechanisms to regulate transmission rates in packet-switched communication networks. We develop a unifying method to study the performance of this general class of finite-buffer state-dependent bulk queueing systems. For this purpose, we use semi-regenerative analysis to develop a numerically stable method for calculating the limiting probability distribution of the queue length process. Based on the limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. We demonstrate our method by means of numerical examples. [ABSTRACT FROM AUTHOR]

We consider an open queueing network consisting of two queues with Poisson arrivals and exponential service times and having some overflow capability from the first to the second queue. Each queue is equipped with a finite number of servers and a waiting room with finite or infinite capacity. Arriving customers may be blocked at one of the queues depending on whether all servers and/or waiting positions are occupied. Blocked customers from the first queue can overflow to the second queue according to specific overflow routines. Using a separation method for the balance equations of the two-dimensional server and waiting room demand process, we reduce the dimension of the problem of solving these balance equations substantially. We extend the existing results in the literature in three directions. Firstly, we allow different service rates at the two queues. Secondly, the overflow stream is weighted with a parameter p ∈ [0,1], i.e., an arriving customer who is blocked and overflows, joins the overflow queue with probability p and leaves the system with probability 1 − p. Thirdly, we consider several new blocking and overflow routines. [ABSTRACT FROM AUTHOR]

The novel core network architecture presented in this paper realizes distributed all-optical switching of payload by partitioning the network into a number of geographically limited domains, where two-way reservations are effective. Thus, inside each domain, loss is eliminated, while traffic from many nodes can be aggregated into single bursts, improving efficiency. Clustered nodes contribute contiguous optical slots, which are marshaled into composite optical frames destined for other clusters, under the guidance of a reservation-based control protocol. The lossless aggregation of traffic from several core nodes allows the use of cost-effective bufferless all-optical transport among the domains with electrical buffers employed at the periphery of the system. The end result is a triple improvement in loss probabilities, efficiency, and cost. This is achieved by exploiting three features of the architecture: the distributed switching functionality (as in early LANs when centralized switching was expensive), localized reservations (avoiding the intolerable delays of end-to-end reservations), and a reduced number of source-destination pairs (by means of node clustering into reservation domains) [ABSTRACT FROM PUBLISHER]

In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples. [ABSTRACT FROM AUTHOR]

In [13], real-time measurements from LANs, variable-bit-rate video sources, ISDN control-channels, the World Wide Web and other communication systems have shown that traffic exhibits a behaviour of self-similar nature. In this paper, we give new lower bounds to buffer-overflow and cell-loss probabilities for an ATM queue system with a self-similar cell input traffic and finite buffer. The bounds are better than those obtained in [20], in an important region of parameters. As in [20], they decay hyperbolically with buffer size, when the latter goes to infinity. However, in some region, a factor which accompanies the decay is higher in this paper than in [20]. [ABSTRACT FROM AUTHOR]

We consider an unbuffered resource having capacity C, which is shared by several different services. Calls of each service arrive in a Poisson stream and request a fixed, integral amount of capacity, which may depend on the service. An arriving call is blocked and lost if there is not enough capacity. Otherwise, the capacity of the call is held for the duration of the call, and the holding period is generally distributed. It is assumed that C and the traffic intensities of the services are commensurately large and asymptotic approximations are obtained for the loss probabilities and their sensitivities to the traffic intensity of each service. These sensitivities are important in optimizing the performance of multiservice, multirate loss networks. Numerical results illustrate the accuracy of the asymptotic approximations. These results show that while prior asymptotic approximations to the loss probabilities are quite accurate, the new approximations are very accurate. Moreover, while the prior asymptotic approximations to the sensitivities are overall rather poor, the new approximations are very good. Experience with case studies has shown that computationally efficient asymptotic techniques are crucial to cope with the size and the number of service offerings of emerging broadband networks in their design and optimization. [ABSTRACT FROM AUTHOR]

A discrete-time, two-server queueing system is studied in this paper. The service time of a customer (cell) is fixed and equal to one time unit. Server 1 provides for periodic service of the queue (period T). Server 2 provides for service only when server 1 is unavailable and provided that the associated service credit is nonzero. The resulting system is shown to model the queueing behavior of a network user which is subject to traffic regulation for congestion avoidance in high speed ATM networks. A general methodology is developed for the study of this queueing system, based on renewal theory. The dimensionality of the developed model is independent of T; T increases with the network speed. The cell loss probabilities are computed in the case of finite capacity queue. [ABSTRACT FROM AUTHOR]

A simple dynamic model helps explain why risk-pooling purchasing arrangements evolved for health, disability, and term life insurance but not for property, automobile, or homeowners' insurance, and why whole-life policies typify life insurance purchased on an individual basis. We show that risk-pooling purchases facilitate insurance against unpredictable changes in one's risk type, but such con- tracts prevail in competitive equilibrium only when the loss probabilities increase with age, as they do for health, disability, and life insurance. In contrast, when the loss probability declines with age (as it does for automobile insurance), then competitive equilibrium entails separating insurance contracts. [ABSTRACT FROM AUTHOR]

Consider an ATM multiplexer where M input links contend for time slots on an output link which transmits C cells per second. Each input link has its own queue of size B cells. The traffic is delay sensitive so B is small (e.g., B=20). We assume that each of the M input links carries Constant Bit Rate (CBR) traffic from a large number of independent Virtual Connections (VCs) which are subject to jitter. The fluctuations of the aggregate traffic arriving at queue i, i=1,..., M, is modeled by a Poisson process with rate λi. The Quality of Service (QoS) of one connection is determined in part by the queueing delay across the multiplexer and the Cell Loss Ratio (CLR) or proportion of cells from this connection lost because the buffer is full. The Oldest Customer(Cell) First (OCF) discipline is a good compromise between competing protocols like round robin queueing or serving the longest queue. The OCF discipline minimizes the total cell delay among all cells arriving at the contending queues. Moreover, the CLR is similar to that obtained by serving the longest queue. We develop QoS formulae for this protocol that can be calculated on line for Connection Admission Control (CAC). These formulae follow from a simple new expression for the exact asymptotics of a M/ D/1 queue. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a multi-server queueing system with heterogeneous customers that arrive according to a marked Markovian arrival process. Customers of two types differ in priorities and parameters of phase type distribution of their service time. The queue under consideration can be used to model the processes of information transmission in telecommunication networks in which often the flow of information is the superposition of several types of flows with correlation of inter-arrival times within each flow and cross-correlation. We define the process of information transmission as the multi-dimensional Markov chain, derive the generator of this chain and compute its stationary distribution. Expressions for computation of various performance measures of the system, including the probabilities of loss of customers of different types, are presented. Output flow from the system is characterized. The presented numerical results confirm the high importance of account of correlation in the arrival process. The values of important performance measures for the systems with the correlated arrival process are essentially different from the corresponding values for the systems with the stationary Poisson arrival process. Measurements in many real world systems show poor approximation of real flows by such an arrival process. However, this process is still popular among the telecommunication engineers due to the evident existing gap between the needs of adequately modeling the real life systems and the current state of the theory of algorithmic methods of queueing theory. [ABSTRACT FROM AUTHOR]

This paper seeks to identify computationally efficient importance sampling (IS) algorithms for estimating large deviation probabilities for the loss on a portfolio of loans. Related literature typically assumes that realised losses on defaulted loans can be predicted with certainty, i.e., that loss given default (LGD) is non-random. In practice, however, LGD is impossible to predict and tends to be positively correlated with the default rate and the latter phenomenon is typically referred to as PD-LGD correlation (here PD refers to probability of default, which is often used synonymously with default rate). There is a large literature on modelling stochastic LGD and PD-LGD correlation, but there is a dearth of literature on using importance sampling to estimate large deviation probabilities in those models. Numerical evidence indicates that the proposed algorithms are extremely effective at reducing the computational burden associated with obtaining accurate estimates of large deviation probabilities across a wide variety of PD-LGD correlation models that have been proposed in the literature. [ABSTRACT FROM AUTHOR]