Pierre M. Fiorini

Asymptotic Behavior of Total Times For Jobs That Must Start Over If a Failure Occurs.

Many processes must complete in the presence of failures. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it may give up on the task and select a replacement task from the ready queue, or it may restart the task. The behavior of systems under the first two scenarios is well documented, but the third (RESTART) has resisted detailed analysis. In this paper we derive tight asymptotic relations between the distribution of task times without failures and the total time when including failures, for any failure distribution. In particular, we show that if the task-time distribution has an unbounded support, then the total-time distribution H is always heavy tailed. Asymptotic expressions are given for the tail of H in various scenarios. The key ingredients of the analysis are the Cramer–Lundberg asymptotics for geometric sums and integral asymptotics, which in some cases are obtained ...

On the completion time distribution for tasks that must restart from the beginning if a failure occurs

For many systems, failure is so common that the design choice of how to deal with it may have a significant impact on the performance of the system. There are many specific and distinct failure recovery schemes, but they can be grouped into three broad classes: RESUME, also referred to as preemptive resume (prs), or check-pointing; REPLACE, also referred to as preemptive repeat different (prd); and RESTART, also referred to as preemptive repeat identical (pri). The following describes the three recovery schemes: (1) RESUME: when a task is fails, it knows exactly where it stops, and can continue from that point when allowed to resume; (2)REPLACE: given a task fails, then when it begins processing again, it starts with a brand new task sampled from the same task time distribution; and, (3) RESTART: When a task fails, it loses all that it had acquired to up to that point and must start anew when upon continuing later. This is distinctly different from (2) since the task must run at least as long as it did before it failed, whereas a new sample, selected at random, might run for a shorter or longer time.

On unreliable computing systems when heavy-tails appear as a result of the recovery procedure

For some computing systems, failure is rare enough that it can be ignored. In other systems, failure is so common that how to handle it can have a significant impact on the performance of the system. There are many different recovery schemes for tasks, however, they can be classified into three broad categories: 1) Resume: when a task fails, it knows exactly where it stops and can continue at that point when allowed to resume (i.e., preemptive resume - prs); 2) Replace: when a task fails, then later when the processor continues, it begins with a brand new task (i.e., preemptive repeat different prd); and, 3) Restart: when a task fails it loses all work done to that point and must start anew upon continuing later (i.e., preemptive repeat identical - pri).In this paper, assuming a computing system is unreliable, we discuss how heavy-tail (hereafter referred to as power-tail - PT) distributions can appear in a jobs task stream given the Restart recovery procedure. This is an important consideration since it is known that power-tails can lead to unstable systems [4], We then demonstrate how to obtain performance and dependablity measures for a class of computing systems comprised of P unreliable processors and a finite number of tasks N given the above recovery procedures.

The effect of different failure recovery procedures on the distribution of task completion times

For a system to be reliable, it must have one or more methods of dealing with failures. Distributed systems face both node failure and communication channel failure. Communication channels, in particular, may suffer failures at a very high rate. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it may restart the task, or it may give up on the task and select a replacement task from the ready queue. These three responses to failure all change the distribution of task completion times. The distribution of completion times is important because it governs mean service time and queue length, and therefore quality of service and buffer size necessary to manage the risk of overflow. The changes to the distribution introduced by the failure response can even turn well behaved exponentially distributed times into powertail distributed times with infinite mean and variance. In this paper we examine the characteristics of distributions that result from restarting after each interrupt, with some discussion of resume and replace, for comparison. We provide analytic and simulation solutions.

Exact Analysis of Some Split-Merge Queues

Computing systems need analytic models to predict performance for a wide range of workloads. In some cases, the system workload can be viewed as a job stream, where each job is split into many synchronized tasks that are processed in parallel at various, possibly heterogeneous, servers. Examples of such systems include, Web service applications, computing systems with redundant disk arrays (RAID), Map– Reduce frameworks, etc. One model that is used to analyze these types of waiting lines is known a split–merge queue, which is a type of synchronized parallel system. Here, on arrival a job is split into n subtasks which are serviced in parallel. Only when all the tasks finish servicing and have rejoined can the next job start. Some analytic results (as well as approximations) can be found in [1, 3, 4]. A related model is the fork–join queue, which is much less analytically tractable. On arrival at the fork point, a job is split into n subtasks which are serviced by each of the n servers. After service, subtasks wait until all other subtasks have also been processed. The subtasks are then rejoined and leave the system. For the split-merge queue, the primary focus of research to date has been on the computation of the moments of the response times in particular the mean. These papers use a method based on the expected maximum order statistic (EMOS) [1, 3, 4]. In some cases, they use EMOS to approximate the performance of fork–join queues since they provide an upper-bound on performance measures. In this study, we obtain an exact representation of the distribution of the maximum order statistic for homogeneous and heterogeneous random variables that have a matrix– exponential (ME) representation, from which the mean and higher moments follow. We can then apply these results to M/G/1, M/G/1/N, M/G/1//N, M/G/C, and G/G/1//N queues where the stationary queue length and response time distributions, and other performance measures can be ascertained for a wide class of split-merge queues. We give examples of subtasks with homogeneous and heterogeneous service time distributions, subtask failure/repair, G/C-type systems, and a variable number of forked subtasks.

Search marketing traffic and performance models

Search Engine Marketing (SEM) is the practice of manipulating and/or paying the search engines (Google, Yahoo!, Bing, etc.) to drive traffic to websites. The SEM community has developed techniques that can channel visitors to websites; however, little work has been done to develop models able to estimate the amount of traffic generated by SEM. In this paper, we develop formulae that can be used to estimate traffic resulting from SEM campaigns that can be used by search marketing agencies for competition analysis and by web hosting providers for performance analysis and capacity planning. Our experimental results show that our models work best for targeted marketing campaigns, but the formulae presented can be generalized to broader marketing domains.

On checkpointing and heavy-tails in unreliable computing environments

In this paper, we discuss checkpointing issues that should be considered whenever jobs execute in unreliable computing environments. Specifically, we show that if proper check-pointing procedures are not properly implemented, then under certain conditions, job completion time distributions exhibit properties of heavy-tail or power-tail distributions (hereafter referred to as power-tail distributions (PT), which can lead to highly-variable and long completion times.

Analytic approximations of fork-join queues

Fork-join queues characterize a network of parallel servers where an arriving job splits into subtasks, and are serviced in parallel. Exact analytic results are known for the mean response time of a two server system. For more than two parallel servers, approximations for the mean response time of both homogeneous and heterogeneous servers have been found. One such approximation is a split-merge queue, which is a type of fork-join queue; and, it is known that the response time yields an approximation and upper bound for the mean response time in the fork-join queue. In this study, we develop a matrix exponential representation of the maximum order statistic of the service time distribution for homogeneous and heterogeneous split-merge queues. We then apply these results to the M/G/1 queue, which enables us to derive the queue length distribution, the response time distribution, and other performance measures for split-merge queues that can be used as approximations and upper-bounds of fork-join queues.

Performance implications of Internet marketing campaigns on Web servers

Internet marketing is the practice of applying marketing techniques to drive traffic to websites. The business community has developed techniques that can generate traffic to websites; however, little work has been done to develop models that assess the performance of web servers resulting from Internet marketing campaigns. From a computer performance standpoint, one challenging aspect of Internet marketing campaigns is they can instantaneously place high demands on the server(s). For example, many campaigns utilize PPC (Pay-Per-Click) engines to market their products, which can generate heavy loads to their server in minutes. Thus, its important for system administrators, web hosting services, providers, etc., to plan appropriately for increased traffic volumes during these campaigns since its well known that user-perceived system performance is often a critical factor determining whether or not customers continue with their online business transaction. In this paper, we develop analytic models that can be used to measure and model the performance impact Internet marketing campaigns on web servers. Our experimental results show that our models work best for highly targeted marketing campaigns; however, the formulations presented can be generalized. We demonstrate our models can be used estimate the traffic to a web site due to SEO and PPC campaigns and show how these models can be used to address web server capacity planning issues.

A Dynamic Authentication Mechanism for Real-Time Network Security

Computers networks are only as secure as the weakest computer system attached to them. Thus, the authentication method used by computers on the network affects its safety. Static authentication methods are applied only once at the beginning of a user session. Unfortunately, these methods provide no protection from the interactions a user has after they are logged on and using the system. An ongoing dynamic authentication supplements an intrusion detection system by recognizing a masquerader, or a legitimate users change of intent. In this paper, we statistically analyze the underlying distributions of the time between user commands and develop an analytic model that emulates the underlying mathematical properties of user behaviors. From this, we show how the probabilities of users executing a sequence of commands during a session can be ascertained. Finally, via our experimental results, we show how the efficacy of dynamic authentication schemes in networked computing environments can be improved by incorporating our techniques.