Efficient Simulation of Population Overflow in Parallel Queues

In this paper we propose a state-dependent importance sampling heuristic to estimate the probability of population overflow in networks of parallel queues. This heuristic approximates the “optimal” state-dependent change of measure without the need for difficult mathematical analysis or costly optimization involved in adaptive methodologies. Comprehensive simulations of networks with an arbitrary number of parallel queues and different traffic intensities yield asymptotically efficient estimates (with relative error increasing sub-linearly in the overflow level) where no other state-independent importance sampling techniques are known to be efficient. The efficiency of the proposed heuristic surpasses those based on adaptive importance sampling algorithms, yet it is easier to determine and implement and scales better for large networks.\u

Efficient Heuristics for the Simulation of Buffer Overflow in Series and Parallel Queueing Networks

Many of recent studies have proved the tail equivalence result for Egalitarian Processor Sharing system: [EQUATION], where B (resp. V) is service requirement (resp. sojourn time) of a customer; for PS, g = 1 - ρ. In this paper, we consider time-shared systems in which the server capacity is shared by existing customers in proportion to (dynamic) weights assigned to customers. We consider two systems, 1) in which the weight of a customer depends on it Age (attained service), and 2) in which the weight depends on the residual processing time (RPT). We allow for a parameterized family of weight functions such that the weight associated with a customer that has received a service (or, has a RPT) of x units is ω(x) = xα for some -∞ < α < ∞. We then study the sojourn time of a customer under such scheduling discipline and provide conditions on α for tail equivalence to hold true, and also give the value of g as a function of α

A spectral theory approach for extreme value analysis in a tandem of fluid queues

We consider a model to evaluate performance of streaming media over an unreliable network. Our model consists of a tandem of two fluid queues. The first fluid queue is a Markov modulated fluid queue that models the network congestion, and the second queue represents the play-out buffer. For this model the distribution of the total amount of fluid in the congestion and play-out buffer corresponds to the distribution of the maximum attained level of the first buffer. We show that, under proper scaling and when we let time go to infinity, the distribution of the total amount of fluid converges to a Gumbel extreme value distribution. From this result, we derive a simple closed-form expression for the initial play-out buffer level that provides a probabilistic guarantee for undisturbed play-out

A dynamic importance sampling method for quick simulation of rare events

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993.Includes bibliographical references leaves 38-39.Simulation of low-probability events may take extremely long times since they occur very rarely. There are various variance reduction methods used to speed up simulations in such cases. In this thesis, a new variance reduction technique is proposed, which is based on expressing the desired probability as the product of a number of greater probabilities and estimating each term in the product in a recursive manner. It turns out that the resulting estimator, when feasible, uses an importance sampling distribution at each step to constrain the samples into a sequence of larger sets which shrink towards the rare set gradually. Moreover, the important samples used in each step are obtained automatically from the outcomes of the experiments in the previous steps. The method is applied to the estimation of overflow probability in a network of queues and remarkable speed-ups with respect to standard simulation are obtained.Erdoğan, AlperM.S

SLA Calculus

For modeling Service-Oriented Architectures (SOAs) and validating worst-case performance guarantees a deterministic modeling method with efficient analysis is presented. Upper and lower bounds for delay and workload in systems are used to describe performance contracts. The SLA Calculus allows one to combine model descriptions for single systems and to derive bounds for reaction time and capacity of composed systems with analytic means. The intended, but not exclusive modeling domain for SLA Calculus are distributed software systems with reaction time constraints. SOAs are a system design paradigm that encapsulate software functions in service applications. Due to their standardized interfaces and accessibility via networks, large systems can be composed from smaller services and presented as services again. A well-known implementation of the service paradigm are Web Services that allow applications with components connected by the Internet. Own services and those rented from providers can be transparently combined by users. Performance guarantees for SOAs gain importance with more complex systems and applications in business environments When a service is rented by a customer the provider agrees upon a Service Level Agreement (SLA) with conditions concerning interface, pricing and performance. Service reaction time in form of delay is an important part in many SLAs and subject to performance models discussed in this work. With SLAs providers implicate a maximum delay for their products when the customer limits the workload to their systems. Hence customers expect the contracted service provider to deliver the performance figures unless the workload exceeds the SLA. Since contract penalties could apply, providers have a natural interest in dimensioning their service in regard to the SLA. Even for maximum workloads specified in the contracts the worst-case delay has to hold. Moreover, due to the compositional nature of Web Services, customers become providers themselves when they offer their service compositions to others. Again, worst-case performance bounds are of major interest here. Analyzing models of SOAs is an option to plan, dimension and validate service performance. For system modeling and analysis many methods exist. Queueing Systems and simulation are two well-known approaches in computer science. They provide average and thus long-term performance numbers quite easily using, probabilistic workload and service process descriptions. Deriving system behavior in worst-case situations for performance guarantees is elaborative and can be impossible for more complex systems. Receiving delay bounds usable in SLAs for SOAs by model analysis is still a research issue. A promising candidate to model SOA with SLAs is Network Calculus, an analytical method to derive performance bounds for network components. Given deterministic descriptions for arrival to and service in a network node hard bounds for network delay and the required buffer memory in routers are computed. A fine-granular separation between short- and long-term goals is possible. Network Calculus models also feature composition of elements and fast analytical analysis. When applied to SOAs with SLAs the problem arises that SLAs are not suitable as a system description and information source for Network Calculus models. Especially the internal service capacity is not exposed by SLAs, since providers consider them as a business secret. Without service process descriptions Network Calculus models cannot be analyzed. The SLA Calculus is presented as a solution to this problem. As a novel contribution for deterministic model analysis for SOAs, SLA Calculus is an extension to Network Calculus. Instead of service process descriptions, it uses information on latency to characterize a system. Delay of services is not a scalar analysis result anymore, it becomes a process over time that is bound with Network Calculus-style curves, the delay curves. Together with arrival curves the performance contracts in SLAs are formalized by so-called SLA Delay Properties (SDPs) as a description for the service performance in worst-case. Service composition can be modeled by serial and parallel combination of SDPs. The necessary theorems for the resulting worst-case bounds are given and proved. We will present a method to transfer these performance figures to the missing service process description again. Apart from basic theory we will also consider solutions for practical modeling situations. An algorithm to extract arrival and delay curves from measurements, enables the modeler to include already existing systems without given SLAs as model elements. Finally, we will sketch a selection method in form of an optimization problem for services to support the dynamic service selection in SOAs with a Service Broker. SLA Calculus model analysis will deliver deterministic upper and lower bounds for workload capacities and response times. For upper bounds the worst-case is assumed, thus bounds are pessimistic. The advantage of SLA Calculus is the ability to compute these bounds very fast and to give system modelers a quick overview on system characteristics considering extreme situations. In other modeling methods a lengthy transient analysis would be required. The strict perspective towards worst-case brought up another analysis target: Until now, relatively little attention was paid to contract conformance between subsequent services within service compositions. When services offer different workload capacities the arrival rate to the system needs to be adjusted to avoid bottlenecks. Additionally, for service compositions no response time contract can be guaranteed without internal buffering to enforce a common arrival rate. SLA Calculus unveils the necessary buffer delays and is able to bound them