General Terms Measurement, Performance, Design, Theory. Keywords Dynamic load balancing, Load sharing, Pareto distribution, 1.

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1 A Dynamic Load Distribution Strategy for Systems Under High Tas Variation and Heavy Traffic Bin Fu Zahir Tari School of Computer Science and Information and Technology Melbourne, Australia {b ABSTRACT Several approaches have been proposed to deal with the issue of load distribution, however they all have similar limitations, such as: (i) tass are executed in an arbitrary order (which may cause large tass to be delayed), (ii) the tas dispatcher does not tae into consideration the server processing capacity (which may cause a large tas to be assigned to a server with low processing power) or (iii) they do not consider tas deadlines (which if not met, may cause tas starvation). This paper proposes an extension of LFF (Least Flow-time First) tas assignment policy [9], called, to deal with these limitations. dynamically computes two priorities, namely tas size and tas size priorities, and put them in a priority based multi-section queue. The testing results clearly show that out performs existing load distribution strategies (that are based on heavy tailed distribution). The testing results also show that more than 80% of tass meet their tas deadline under. General Terms Measurement, Performance, Design, Theory. Keywords Dynamic load balancing, Load sharing, Pareto distribution, 1. INTRODUCTION Due to uneven tas arrival in distributed systems, it is possible for a system to be heavily used in one node, while lightly loaded or even idle in other nodes. To improve the overall system performance, which is characterized by the system response time and the maximal system throughout, two load distribution strategies are proposed in the past years: load balancing and load sharing. The load balancing strategies attempt to equalize the worload among nodes, whereas the load sharing strategies attempt to minimize the chance of idle nodes while other tass wait for service. Computer loads have been traditionally modelled by an exponential distribution and tass arrival rate follows the Poisson distribution. With Permission to mae digital or hard copies of all or part of this wor for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SAC 2003, Melbourne, Florida, USA ACM /03/03 $5.00. this assumption, early research wor on load distribution (e.g. [11]) showed that the shortest queue tas assignment policy is optimal. However some recent wor [4][10][5][9] demonstrated that the tas size distribution in computer loads has a higher variability than is predicted by exponential distribution models. The tas distribution observed in real-world systems often follows what is nown as a heavy-tailed distribution, where tass have high size variation. Such high size variation can be found, for example, in FTP transmissions over the Internet [7] and files stored in Unix file systems [6]. Several load distribution strategies have been proposed to handle tas loads with a heavy-tailed distribution. (Size Interval Tas Assignment with Equal load) [4], Least Loaded First () [8] and Least Flow-Time First (LFF) [9] policies are probably the most well nown approaches that handle tas loads with a heavy-tailed distribution. defines the size range associated with each server so that the total load assigned to each server is the same. One of the main limitations of is that it does not consider the server load. Similarly, strategy, which assigns a tas to the least loaded server, does not server capacity. LFF deals with such a limitation of and dispatches tass to the server with the least mean flow time. Each server maes use of a multi-section queue to order tass based on their size. Then tass are allocated based on their size and the server capacity. LFF indeed provides better performance than and, however it lacs for the support for important features, such as deadlines and tas priorities. Another important limitation of, and LFF is that they do not provide a load index to calculate the flow time of tass, which of course has an impact on the performance. This paper focuses on the limitations of LFF and proposes an extension to deal with tas priorities and tas deadlines. The proposed approach is called. Two tas priorities are dynamically computed, namely tas size priority and tas deadline priority. The former is computed based on the size of tass and is used by the central dispatcher to decrease the mean waiting time and mean slow down of (small) tass. The tas deadline priority is computed based on several parameters, such as the time it taes to allocate a tas to a server, the actual processing time and the slac time of a tas. A central dispatcher is used to collect load index information, calculate the flow time of tass at each server, and later assigns tass to appropriate servers. A priority manager is used at each server to order the tass based on their corresponding deadlines and sizes. Tass are put into a priority based multisection queue and then executed in priority order. As shown in later sections, outperforms,, LFF and. In particular, when the tas size

2 variation is very high (i.e. α=1.1, where α represents the variability of tass), performs two to four times better than in terms of flow time and waiting time. The mean slowdown of tass under the policy is much less than under the policy. We also found that under the, and policies, the percentage of tass that meet their time deadlines is low. On the contrary, more than 80% of tass meet their time deadlines under the policy. This is because considers tas deadlines when setting tas execution priorities, and therefore the tas starvation problem is minimised. The rest of this paper is organised as follows. Section 2 overviews some of the well-nown load distribution techniques for heavy-tail distribution. Section 3 describes the proposed policy in detail. Section 4 discusses the experiment results and Section 5 concludes on our future wor on. 2. RELATED WORK Crovella [1] proposed SITA-V (Size Interval Tas Assignment with Variable Load) which operates different hosts with different loads. Smaller tass under SITA-V are dispatched to the least-loaded servers, whereas the few large tass are sent to the servers that are more highly loaded. This load distribution policy wors well when the tas variation is very high (α [ ], where α denotes the tas variation) because it unbalances the load so that most of the tass can be processed quicly on the under-loaded server. Therefore a small fraction (but large sized) tass are processed on the overloaded server. The mean slowdown time 1 of a tas in SITA-V can be significantly improved. SITA-V however has substantial limitation when the tas variation is not too high but closer to the empirical measurement, i.e. 0.9<α< 1, as the average size of small tass is increased and there is no more room to reduce the variation. Another limitation of SITA-V is that when the system load is very high, the mean slowdown does not improve as much as in a low system load. If a server is overloaded, SITA-V performs poorly. Unbalancing the load will also increase the waiting time of tass in the queue of heavily loaded servers. The tradeoff between decreasing the mean waiting time and increasing mean slowdown shows that SITA-V is only useful when the server load is low and the tas variation is very high, which seriously limits its applicability. Another well-nown load distribution strategy is TAG (Tas Assignment based on Guessing Size) [3]. Basically TAGS assigns a time limit with each server and the size of tass are not nown a priori. Upon arrival a tas is executed at a server up to the designated time limit associated with the server. If the tas cannot be finished within the time limit, this will be stopped and restarted at a new server. TAGS provides performance improvement by unbalancing the load as most of the small tass can be finished within the time limit. Therefore only a small number of large tass need to be restarted in a new server. TAGS wors well when the tas variation is high and system load is not too high. However when the system load is high, large tass will be restarted multiple times and therefore dramatically affects the overall performance of a system. 1 A mean slow down of a tas is equal to waiting time divided by tas size. (Size Interval Tas Assignment with Equal Load) [4] dealt with the limitations of TAG. The main idea of is that each host in a distributed server system is assigned a separate range of tas sizes so that the total load for each host is the same. Upon arrival, each tas is associated with a range and assigned to the host that handles tass in that range. The policy is intended to eep small tass from getting stuc behind large tass. When comparing with Least Loaded First (), shows better performance when the tas size variation is low (α is large). However when the tas size distribution shows a high variance, suffers from exponential explosion of slowdown. The performance policy is relatively unchanged over a wide range of α. The reason is that by setting a range of tas sizes handled by each server, reduces the tas size variability and therefore improves the system performance. Note that under the policy, most of tass are sent to the servers that handle smaller tass, and a small number of large tass are sent to the servers that handle larger tass. This can improve the slowdown because the waiting time of small tass will not be affected as much by large tass. is a static approach (i.e. the range of tas sizes a server handles is predetermined), which maes it relatively easy to implement. However if the tas size distribution changes over time, it cannot dynamically change the size range handled by each server. does mae no-realistic assumptions by assuming that all servers should the same processing capacity. Another problem with is that under a Pareto distribution, large tass will always be sent to the server that handles larger tass. This will cause these servers to be overloaded and therefore the waiting time for large tass will be increased significantly. In the case of tas sizes with heavy-tailed distribution, large tass (which represent 20% of the total tass) tae more than 80% of the CPU. The delay of large tass will therefore affect the mean waiting time considerably. LFF (Least Flow Time First) [9] addresses the drawbacs of by considering the capacity and flow time of each server. LFF assigns a tas to the server with the least flow time for that tas. Each server uses a size-based queue to order the tass in smaller-tass-first order. The simulation results showed substantial performance improvement over and for most of the existing sized-based approaches. LFF policy provides a good basis for dealing with load distribution by considering the server capacity, server load and tas size. However LFF does not consider tas deadlines. Since tass are only ordered by size, large tass will be punished and starvation can be caused for these tass. 3. APPROACH is an extension of LFF to deal with tas priority and deadline. Section 3.1 introduces some basis definitions needed to formalise the proposed approach and Sections 3.2 and 3.3 describe the model and it mathematical formalisation. Section 3.4 overviews the main features of the model. 3.1 Basics In a heavy-tailed distribution, there are typically only a few large tass. This distribution is formalised as follows: 0<_<2, where _ denotes the variability of the

3 tas size. The simplest heavy-tailed distribution is the Bounded Pareto distribution [1], which is defined as α α α 1 f ( x) = x x p α 1 ( / p) where is the smallest possible tas size and p is the largest possible tas size. In our model, we assume that tas size follows the Bounded Pareto distribution. To mae the tas distribution approximate the Pareto distribution, is set to 100 and p to 1,000,000. The tas arrival rate follows a Poisson distribution with arrival rate _. We also assume that the tas size is nown upon arrival and that tass are indivisible and cannot be pre-empted. We will use the following definitions in the remaining parts of this paper. Deadline: it refers to the time by which a tas should be finished. There are two inds of deadlines: hard deadline and soft deadline. For the hard deadlines, each tas must strictly follow the deadline requirement. If a tas cannot finish before the deadline, it must be abandoned. For the soft deadlines, the server maes a "best effort" attempt to meet the deadline of a given tas, but if it fails to meet the deadline, it should continue to process the tas rather than simply abandon the service request. Throughout this paper, when we refer to a deadline, we will use the soft deadline semantic. Flow time: It represents the total time a tas taes to be processed, including the processing and the waiting time. Formally a flow time of a tas T is equal to Slow down: It is defined as the waiting time divided by the tas size, namely Slowdown T ) = WaitingTime( T ) Size( T ) ( 3.2 Distributed Server Model When a tas is assigned to a server, this will be put in the server s queue. The server will execute tass in order based on the tas priority. The local tas manager assigns a priority for each arriving tas and maintains a multi-section queue based on the priority. The queue with the highest priority will be processed first. Within a priority queue, the tas with the smallest tas size will be processed first. The tas priority is determined by two factors, size and deadline. The priority of a tas T is defined as Priority(T ) = prioritysize(t ) + prioritydeadline(t ) where prioritysize(t ) and prioritydeadline(t ) are determined by the tas size and deadline respectively. Tass with a higher priority are executed before tass with a lower priority. Where there is more than one tas with the same priority, smaller tass are executed before larger tass. If tass have the same size and priority, then they will be processed based on a First Come, First Served (FCFS) basis Tas Size Priority If tass are executed in the order they are generated, the small tass will always be delayed by larger tass. Therefore the mean waiting time of the small tass is increased and the mean slowdown of the small tass is larger. Normally smaller tass should finish sooner because they are small, and large tass can be delayed without penalty because they are larger. So smaller tass should have a higher priority than larger tass if all other conditions are the same. Based on these points, we set a 4-level priority queue based on tas size, as shown in Table 1. Tas Size Range Level of Importanc e [ ) Small 4 [1,000 10,000) Medium 3 [10, ,000) Large 2 [100,000 1,000,000 ] Huge 1 Table 1: Tas Size Priority Factor Priority Factor We assume that the smallest tas size (which is denoted by ) is 100 and the largest tas size (which is denoted by p) is 1,000,000. The tass with a higher priority (corresponding to smaller tas size) should be processed before tass with a lower priority, if the other conditions are the same Tas Deadline Priority The other factor in determining the tas priority is the tas deadline. When generated, each tas is assigned a deadline. The deadline of a tas T is composed of three parameters, namely Alloctate(T ): it represents the time it taes to allocate a tas to a server; Process(T ): it is the actual processing time of the tas. It is a value that is dependent on tas size and the server on which it is executed. Flex(T ): it represents the slac time of the tas, which indicates how long a tas can be delayed before it will fail to meet its deadline. It reflects the importance of a tas. The lower the slac time, the more important the tas is. Formally, the tas deadline priority is defined as follows: Deadline(T ) = Allocate(T )+ Process(T )+ Flex(T ) The deadline s priority is set (by the Tas Generator) according to the different levels shown in Table 2. If a tas has not been assigned a deadline by the tas generator, it is considered to be an ordinary tas, with an unbounded flextime. When a tas is required to be finished by a certain time, the priority is set to the appropriate level, as shown in Table 2. A few tass may need to be processed more quicly than other tass, so should be assigned the priority of an urgent or very urgent tas. However, in most cases, tass will not have deadlines. The range is set based on the flextime and processing time. Since in tas deadline decision-maing, the tas flextime is more important than processing time, we tae it as a major factor when setting the priority. For two tass with the same size, the greater the flextime, the lower the priority. Note that tass that do not have a deadline are regarded as ordinary tass. Tas deadline (time units) Level of Importance Priority Factor [0 100) Very urgent 4 [100 1,000) Urgent 3 [1, ,000) Important 2 [100,000 + ) Ordinary 1 Table 2: Deadline Priority Factor.

4 3.3 Mathematical Model examines the flow time and tas priority of tass to determine how to assign and process a tas. In this section, we will show how to calculate the flow time of a tas. To assign a tas to the most appropriate server, we need to now the load index of each server. For the Pareto tas size distribution, the tas queue can be classified as a M/G/c queue [12], where M means the tas arrival rate follows the Poisson distribution with tas arrival rate λ, G refers the general tas size distribution, which in this case is the Bounded Pareto Distribution, and c represents the number of servers in the distributed system. Using an M/G/c queue, we need to calculate the waiting time and processing time. The waiting time in policy is defined by the server load, expected numbers of tass, tas priority and tas arrival rate. The expected waiting time of tas T with size x can be expressed as follows: where _ is the arrival rate of the tass and p λ xf ( x) dx is the total of tas size in the queue. processcap abilityfactor is the server process capacity normalised by CPU, RAM, and cache size. _ is the system load in a distributed server farm and is defined in [9] as E{ T } = λ where ρ E { T } is the mean tas size h and h is the number of servers in the server farm. The Processing time is related to tas size and server capacity, and is defined as: where λ xf ( x) dx E{ ProcessingTime( T )} = n processcapabilityfactor p xf ( x) dx is the total of tas sizes in the queue and n is the total number of tass in the server p performance results, including performance for over-loaded systems, can be found in [2]. 4.1 Performance in Under-Loaded Systems Figures 1, 2 and 3 show the results when the system load is 0.4, 0.6 and 0.8 respectively. is the probably the worst policy as its flow time is always very high because it assigns tass on the basis of probability. It does not consider the server status or the size of the tass. As the tas variation gets higher, the waiting time, slow down and the flow time are all extremely high, which causes serious tas delays. and policies both perform better than. shows a better waiting time and flow time than when the tas variation is heavy-tailed (α 1.3). dynamically determines the load of each server and sends the tas to the server with the shortest waiting queue. Therefore the waiting time is decreased under. However, the slowdown under deteriorates as tass are executed in the order they arrive. This means that usually small tass have to wait until a very large tas finishes before they can be executed. In contrast, outperforms in terms of slowdown, especially when the tas distribution is heavytailed. This is because uses a static size based strategy and when the tas variation is high, most tass are going to the same server and large tass are sent to other servers. This may cause some tass have to wait for a longer time but the slowdown is decreased since in a particular server. The flow time of a tas T is then is defined as: FlowTime ( T ) = E{ WaitingTime( T )} + E{ ProcessingTime( T )} When the load index collector in the tas dispatcher sends a request to a server for the load index, the server will return the load index based on the mean flow time to the dispatcher. 4. TESTING RESULTS We have implemented and compared it performance with existing load distribution policies, namely, [4] and Dynamic Least Loaded First [9]. Experiments are performed under a range of system loads from underload to overload. For a particular load scenario, α was varied from 1.1 to 2.0, which reflects a tas variation ranging from high (1.1 α 1.3) to low (1.4 α 2.0). In each case the same set of 5000 tass was produced based on the bounded Pareto distribution, and three well-nown policies and the proposed policy were used to assign the tass. The flow time, waiting time and slowdown for each tas was recorded, and the mean value in each case was calculated. These performance results for under-loaded systems and heavy tail are shown in Figures 4 and 5. A complete set of

5 Mean Waiting Time Mean Slowdown Mean Slowdown á (System Load = Mean Flow Time Figure 1: Mean waiting time, mean slowdown and mean flow time when the system load = 0.4 and _ varies from 1.1 to 2.0. When the tas variation is high, has the best flow and waiting time. Tass are prioritised at the server based on the tas size and tas deadline, because a tas with higher deadline requirements cannot wait for a long period. When α 1.3, the slowdown of is always less than 15, which is lower than and. Figure 2: Mean waiting time, mean slowdown and mean flow time when the system load = 0.6 and _ varies from 1.1 to 2.0. Figures 2 and 3 show the results when the system load is 0.6 and 0.8 respectively. The results are similar to when the system load is 0.4. also performs well under these conditions. When the system load is 0.6 and the tas variation is high (α 1.3), the mean waiting time of the policy is six times smaller than the, and two times smaller than and.

6 Mean Waiting Time achieves even better performance in terms of slowdown than because tass are allocated on the basis of least flow time, and executed on the basis of priority. This leads to tass being processed on the most capable server with the shortest waiting queue. Thus a balance between waiting time and processing capability is achieved. Therefore even when system load increases, the mean slowdown is still lower compared to and. Performance is also improved because tas deadlines are considered when determining tas priority, which helps avoid tas starvation Mean Flow Time Figure 3: Mean waiting time, mean slowdown and mean flow time of the four policies when the system load = 0.8 and _ varies from 1.1 to Performance When Tas Distribution is Heavy-Tailed This section discusses the performance of the four policies under the typical heavy-tailed distribution where the _ value is fixed at 1.1. Because the random policy is obviously the worst choice due to its simplistic algorithm, we will only discuss the, and policies. Figure 4 shows the performance of the three policies at system loads ranging from 0.4 to 1.3. The testing results have shown that the performance of all three policies decreases as the system load increases. However with this tas distribution, the performance of is much better than the other two policies, regardless of the system load. We also note that the slowdown of tass under increases much faster than and when the system load varies from the medium load (system load =0.6) to the overload (system load =1.1). This is because under high system load, even the least loaded server will have a very long waiting queue, so that cannot show its advantages of dynamic tas allocation. The tass might be sent to a server with a relatively low processing capacity although the remaining processing time at that server is the shortest. Therefore the tass are delayed due to the smaller server capacity and the long waiting queue. addresses this limitation to some extent, by setting tas size ranges for the server and assigning tass to the servers based on their sizes. Therefore under a heavy-tailed distribution, most small tass can be processed quicly by grouping them by tas size. Therefore large tass can bear longer delay so that the mean slow down is lowered. Mean Slowdown Figure 4: Mean waiting time, mean slowdown and mean flow time of the four policies under different system loads _ is fixed at 1.1, which reflects a typical heavy-tailed distribution. 4.3 Tas Time Deadlines Figure 5 depicts the percentage of tass that meet their deadlines, under the four policies, and for different system loads. We found that when the system load is 0.4, only 35% of tass under meet their deadlines because this policy assigns tass based on the probability that serious tas delays are caused. Many tass with earlier deadlines are delayed by the few very large tass, so that their time deadlines cannot be meet. and perform better than. When the

7 system load is 0.4, 62% of tass under and 60% of tass under meet their deadlines (see Figure 5). This is because assigns tass to the least loaded server, and therefore the tas waiting time is reduced. Tass get processed more quicly and the probability that deadlines will be met is higher. By assigning tass in a certain range to certain servers, effectively reduces the tas variation of tass presented to each server. This means that for each server, small tass will not be delayed by large tass. In general, small tass benefit from lower mean slowdown and deadlines of small tass can be met only when tass are assigned to the server with a lower load. However, does not consider server load, so especially in the case where system load is high, a tas might be assigned to a server with a long waiting queue. In this case, time deadlines may be missed because of the delayed execution of tass. 0%20%40%60%80%100% Figure 5: The percentage of tass that meet their deadline. achieves the best tas deadline result. When the system load is 0.4, more than 85% of tass meet their deadline. Even if the system load is increased, the LFF- PRIORITY results are still much better than the others policies. This is because the deadline of a tas is considered when calculating tas priority. For a given size, a tas with an earlier deadline will get a higher priority over a tas with a later deadline, and will be processed earlier. This helps ensure that the tas will meet the deadline requirement. In a heavy-tailed distribution we also need to consider tas size as one of the factors when determining the priority, so that if two tass have the same deadline, the server will execute the smaller tas first. This is why under the policy, not all tass can meet their deadlines. However the policy still ensures that most tass can be executed in time. 4.4 Discussion As demonstrated in the previous section, policy offers better performance than the other three policies. When the system load is very low (e.g., load = 0.4) and α is in the range of 1.1 to 1.3, outperforms in terms of waiting time by as much as two times. When tas variation is high, it also reduces the slowdown dramatically, compared with. also exhibits good mean flow time characteristics. The central dispatcher maes use of the load index at each server to calculate the current flow time of a tas. The flow time considers both the tass queued on a server, and the processing capacity of the server. Therefore it can schedule tass to the server with the shortest waiting queue and highest processing capacity. Note that even when the system load is very high or even overloaded, still performs better than the other policies because the load index reflects the server s current status, so based on this information the dispatcher can better assigning the tass to the most suitable server. The LFF-Size policy [9] may cause tas starvation since it orders tass only by size. Because in a heavy tailed distribution more than half of the tass are small tass, ordering tass based only on size may cause large tass to be delayed indefinitely. If a large tas is not be finished by a certain time, it will may lead to the failure of the system to meet the deadline of that tas since it cannot have a chance to be executed. The policy addresses the starvation of large tass by allocating tass so as to minimise flow time, and determining the execution order of tass queued on a server by considering tas size and deadline. During the simulation we find that under the policy, more than 80% of tas deadlines are met, while the mean waiting time, mean slowdown and mean flow time per tas is still much better than and. This result justifies our conclusion that the policy can achieve better performance without compromising tas deadlines. 5. CONCLUSION This paper investigates tas assignment and execution policies in heterogeneous distributed systems under high tas variation. Some of the major tas assignment policies were discussed and their advantages and drawbacs presented. We have also showed that Least Loaded First () [8] [9] policy has the advantage of dynamically assigning tass to the server with the least remaining wor, and that the waiting time under is lower than other existing policies. However does not consider differing server processing capacities or tas priorities. On the other hand the Size Interval Tas Assignment with Equal Load () [4] policy achieves a better mean slowdown because it reduces the tas size variation by assigning a size range to each server in the system. However the waiting time and flow time under is not as good as because it simply assigns tass based on size and does not consider the server load. This may lead to some tass being assigned to heavily loaded servers. Therefore the waiting time of tass will be longer and tas deadlines may be missed. Analysing the limitations of LFF [9], we have proposed as an extension of this policy. Essentially, has a central tas dispatcher that assigns tass to the server with the least flow time for that tas. To calculate the flow time, the system has a load index at each server, which the dispatcher can retrieve. The dispatcher uses this information to mae allocation decisions. Upon arrival at each server, the tass are assigned a priority based on tas size and deadline, and put into a priority queue. This queue then determines the order in which the tass will be executed. To compare the performance of against the, LFF and policies, we fed a predetermined set of tass to a simulation of the policies, then measured the mean waiting time, mean slowdown and mean flow time per tas. We also observed how many tass met their deadlines under each of the policies. We found that in systems of this nature under these conditions, has better performance than the other three policies in all of the above measurements. The policy performs especially well when the tas size variation is high (α 1.3). We also see that the deadlines of tass are well met under.

8 There is however some limitations with. One of them is that if the system load is very high and tas variation is not high, the policy performs unsatisfactorily, because it tries to balance tas size and deadline. This may cause some smaller tass to be delayed by larger ones. Another limitation is that the policy does not consider the issue of tas interdependency. If some tass are dependent on other tass, the order of dependency must be maintained in spite of tas sizes and tas deadlines. ACKNOWLEDGMENTS This project is fully supported by the ARC Discovery Grant no. DP awarded by the Australian Research Council (ARC) for REFERENCES [1] M. E. Crovella, M. Harchol-Balter and C. Murta, Tas Assignment in a Distributed System: Improving Performance by Unbalancing Load, Proc. of ACM SIGMETRICS Conference on Measurement and Modelling of Computer Systems, , [2] B. Fu and Z. Tari, Dynamic Load Balancing for Systems under Heavy Traffic Load and High Tas Variation, Technical report, RMIT University, School of Computer Science, Melbourne, Australia, November [3] M. Harchol-Balter, Tas Assignment with Unnown Duration, Proc. of the 20 th Int. Conf. on Distributed Computing Systems (ICDCS), Taipei, , [4] M. Harchol-Balter, M. E. Crovella and C. Murta, On Choosing a Tas Assignment Policy for a Distributed Server System, Journal of Parallel and Distributed Computing, , [5] M. Harchol -Balter and A. Downey, Exploiting Process Lifetime Distributions for Dynamic Load Balancing, Proc. Of ACM SIGMETRICS Conference on Measurement and Modelling of Computer Systems, 13-24, [6] G. Irlan, Unix file Size Survey 1993, [7] V. Paxson and S. Floyd, Wide-area traffic: The Failure of Poisson Modelling, IEEE/ACM Transactions on Networing, , [8] K. G. Shin and C. J. Hou, Design and Evaluation of Effective Load Sharing in Distributed Real-Time Systems, IEEE Transactions on Parallel and Distributed Systems, 5(7), , [9] L. Tan and Z. Tari, Dynamic Tas Assignment in Server Farms Better Performance by Tas Grouping, Proc. of the International Symposium on Computers and Communications, [10] J. Watts and S. Taylor, A Practical Approach to Dynamic Load Balancing, IEEE Transactions on Parallel and Distributed Systems, 9(3), , [11] W. Winston, Optimality of the Shortest Line Discipline, Journal of Applied Probability, 14: , [12] J. A. White, J. W. Schmidt and G. K. Bennett, Analysis of Queuing Systems, Academic Press, Inc. (London) Ltd. Chapters 1-5, 1975.

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