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Mean Value Technique for Closed ForkJoin Networks
 PROCEEDINGS OF ACM SIGMETRICS CONFERENCE ON MEASUREMENT AND MODELING OF COMPUTER SYSTEMS
, 1999
"... A simple technique for computing mean performance measures of closed singleclass forkjoin networks with exponential service time distribution is given here. This technique is similar to the mean value analysis technique for closed productform networks and iterates on the number of customers in t ..."
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Cited by 13 (3 self)
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A simple technique for computing mean performance measures of closed singleclass forkjoin networks with exponential service time distribution is given here. This technique is similar to the mean value analysis technique for closed productform networks and iterates on the number of customers in the network. Mean performance measures like the mean response times, queue lengths, and throughput of closed forkjoin networks can be computed recursively without calculating the steadystate distribution of the network. The technique is based on the mean value equation for forkjoin networks which relates the response time of a network to the mean service times at the service centers and the mean queue length of the system with one customer less. Unlike productform networks, the mean value equation for forkjoin networks is an approximation and the technique computes lower performance bound values for the forkjoin network. However, it is a good approximation since the mean value equation is derived from an equation that exactly relates the response time of parallel systems to the degree of parallelism and the mean arrival queue length. Using simulation, it is shown that the relative error in the approximation is less than 5% in most cases. The error does not increase with each iteration.
Integrated performance models for SPMD applications and MIMD architectures
 IEEE Trans. on Parallel and Distributed Systems
, 2002
"... Abstract—This paper introduces queuing network models for the performance analysis of SPMD applications executed on generalpurpose parallel architectures such as MIMD and clusters of workstations. The models are based on the pattern of computation, communication, and I/O operations of typical parall ..."
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Cited by 7 (1 self)
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Abstract—This paper introduces queuing network models for the performance analysis of SPMD applications executed on generalpurpose parallel architectures such as MIMD and clusters of workstations. The models are based on the pattern of computation, communication, and I/O operations of typical parallel applications. Analysis of the models leads to the definition of speedup surfaces which capture the relative influence of processors and I/O parallelism and show the effects of different hardware and software components on the performance. Since the parameters of the models correspond to measurable program and hardware characteristics, the models can be used to anticipate the performance behavior of a parallel application as a function of the target architecture (i.e., number of processors, number of disks, I/O topology, etc). Index Terms—Single program multiple data (SPMD), multiple instruction multiple data (MIMD), performance model, queuing network model, forkjoin queues, mean value analysis (MVA), parallel I/O, synchronization overhead, speedup surface. 1
The M/M/1 forkjoin queue with variable subtasks
"... The forkjoin queue models parallel resources where arriving jobs divide into various number of subtasks that are assigned to unique devices within the parallel resource. Each device in the parallel resource is modeled ¢¡ £ ¢¡¥ ¤ by queueing servers. A job completes execution and departs the para ..."
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Cited by 4 (0 self)
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The forkjoin queue models parallel resources where arriving jobs divide into various number of subtasks that are assigned to unique devices within the parallel resource. Each device in the parallel resource is modeled ¢¡ £ ¢¡¥ ¤ by queueing servers. A job completes execution and departs the parallel resource after all its subtasks complete execution. This paper analyzes ¦server forkjoin queues where arriving jobs divide into ¤¨§�©�§ are assigned to unique servers of the forkjoin queue. There is no known closedform solution for ¦��� � forkjoin queues. The paper presents an O(log K) algorithm for computing the mean response time pessimistic and optimistic bounds and for computing the mean response time approximation of the forkjoin queue. The error bounds for the response time bounds and approximation are presented. Index Terms: forkjoin synchronization, performance evaluation, parallel computer and storage systems. 1
Generalized class C Markov chains and computation of closedform bounding distributions
 PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES
"... In this paper, we first give a characterization of a class of probability transition matrices having closedform solutions for transient distributions and the steadystate distribution. We propose to apply stochastic comparison approach to construct bounding chains belonging to this class. Therefore ..."
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Cited by 2 (1 self)
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In this paper, we first give a characterization of a class of probability transition matrices having closedform solutions for transient distributions and the steadystate distribution. We propose to apply stochastic comparison approach to construct bounding chains belonging to this class. Therefore bounding chains can be analyzed efficiently through closedform solutions in order to provide bounds on the distributions of the considered Markov chain. We present algorithms to construct upper bounding matrices in the sense of the ≤st and ≤icx order.
Geometric Bounds: a NonIterative Analysis Technique for Closed Queueing Networks
, 2008
"... We propose the Geometric Bounds (GB), a new family of fast and accurate noniterative bounds on closed queueing network performance metrics that can be used in the online optimization of distributed applications. Compared to stateoftheart techniques such as the Balanced Job Bounds (BJB), the GB ..."
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Cited by 2 (0 self)
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We propose the Geometric Bounds (GB), a new family of fast and accurate noniterative bounds on closed queueing network performance metrics that can be used in the online optimization of distributed applications. Compared to stateoftheart techniques such as the Balanced Job Bounds (BJB), the GB achieve higher accuracy at similar computational costs, limiting the worstcase bounding error typically within 5%−13 % when for the BJB it is usually in the range 15%−35%. Optimization problems that are solved with the GB bounds return solutions that are much closer to the global optimum than with existing bounds. We also show that the GB technique generalizes as an accurate approximation to closed forkjoin networks commonly used in disk, parallel and database models, thus extending the applicability of the method beyond the optimization of basic productform networks.
A Matrix Pattern Compliant Strong Stochastic Bound
"... Stochastic bounds are a promising method to analyze QoS requirements. Indeed it is sufficient to prove that a bound of the real performance satisfies the guarantee. However, the time and space complexity issues are not well understood so far. We propose a new algorithm to derive a strong stochastic ..."
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Cited by 1 (1 self)
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Stochastic bounds are a promising method to analyze QoS requirements. Indeed it is sufficient to prove that a bound of the real performance satisfies the guarantee. However, the time and space complexity issues are not well understood so far. We propose a new algorithm to derive a strong stochastic bound of a Markov chain, using a matrix pattern specifing the structural properties a bounding matrix should comply with. Thus we can obtain a simpler Markov chain bounding for which the numerical computation of the steadystate solution is easier. 1.
Design Alternatives for LargeScale Web Search: Alexander was Great, Aeneas a Pioneer, and Anakin has
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Trading off subtask dispersion and response time in splitmerge systems
 In Analytical and Stochastic Modeling Techniques and Applications (ASMTA’13), volume 7984 of Lecture Notes in Computer Science
, 2013
"... Abstract. In many realworld systems incoming tasks split into subtasks which are processed by a set of parallel servers. In such systems two metrics are of potential interest: response time and subtask dispersion. Previous research has been focused on the minimisation of one, but not both, of these ..."
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Cited by 1 (1 self)
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Abstract. In many realworld systems incoming tasks split into subtasks which are processed by a set of parallel servers. In such systems two metrics are of potential interest: response time and subtask dispersion. Previous research has been focused on the minimisation of one, but not both, of these metrics. In particular, in our previous work, we showed how the processing of selected subtasks can be delayed in order to minimise expected subtask dispersion and percentiles of subtask dispersion in the context of splitmerge systems. However, the introduction of subtask delays obviously impacts adversely on task response time and maximum sustainable system throughput. In the present work, we describe a methodology for managing the trade off between subtask dispersion and task response time. The objective function of the minimisation is based on the product of expected subtask dispersion and expected task response time. Compared with our previous methodology, we show how our new technique can achieve comparable subtask dispersion with substantial improvements in expected task response time.
A model of periodic acknowledgement
, 2000
"... We study a problem abstracted from modeling a multicast protocol. In our model, messages generated by a single source are simultaneously forwarded to a set of receivers where they are independently processed. We assume a statedependent message arrival rate and memoryless service time distributions. ..."
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We study a problem abstracted from modeling a multicast protocol. In our model, messages generated by a single source are simultaneously forwarded to a set of receivers where they are independently processed. We assume a statedependent message arrival rate and memoryless service time distributions. The receivers may process messages at different average rates. Messages processed by all receivers are periodically acknowledged and cleared from the system. Due to finite buffer space, the total number of nonacknowledged messages in the system is limited. Our focus in this paper is on the number of messages cleared at acknowledgement time. The problem under consideration bears resemblance to a fork/join process with heterogeneous servers, used in the study of multiprocessing computer systems. Our model includes the additional features of finite buffer space and delayed periodic departure of completed jobs. Even without these features, the resulting type of queuing model has no known closedform solution in the general case of more than two servers. Because the arrival processes to the servers are correlated, the model is difficult to decompose. We propose a relatively simple decomposition technique and a fixedpoint iteration scheme. In our approach, we consider each receiver (server) in isolation, and we account for the influence of other receivers through the probability that a given number of messages can be cleared at acknowledgement time. We derive elementary differential equations for the number of messages processed by a receiver. These equations involve the conditional probability of the number of messages
Reduction of Subtask Dispersion in ForkJoin Systems
"... Abstract. Forkjoin and splitmerge queueing systems are wellknown abstractions of parallel systems in which each incoming task splits into subtasks that are processed by a set of parallel servers. A task exits the system when all of its subtasks have completed service. Two key metrics of interest ..."
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Abstract. Forkjoin and splitmerge queueing systems are wellknown abstractions of parallel systems in which each incoming task splits into subtasks that are processed by a set of parallel servers. A task exits the system when all of its subtasks have completed service. Two key metrics of interest in such systems are task response time and subtask dispersion. This paper presents a technique applicable to a class of forkjoin systems with heterogeneous exponentially distributed service times that is able to reduce subtask dispersion with only a marginal increase in task response time. Achieving this is challenging since the unsynchronised operation of forkjoin systems naturally militates against low subtask dispersion. Our approach builds on our earlier research examining subtask dispersion and response time in splitmerge systems, and involves the frequent application and updating of delays to the subtasks at the head of the parallel service queues. Numerical results show the ability to reduce dispersion in forkjoin systems to levels comparable with or below that observed in all varieties of splitmerge systems while retaining the response time and throughput benefits of a forkjoin system.