NAND flash storage is widely adopted in all classes of computing devices. However, random write performance and lifetime issues remain to be addressed. In this paper, we propose a novel buffer replacement algorithm called TS-CLOCK that effectively resolves the remaining problems. Our experimental results show that TS-CLOCK outperforms state-of-the-art algorithms in terms of performance and lifetime.
{"title":"TS-CLOCK: temporal and spatial locality aware buffer replacement algorithm for NAND flash storages","authors":"Donghyun Kang, Changwoo Min, Y. Eom","doi":"10.1145/2591971.2592028","DOIUrl":"https://doi.org/10.1145/2591971.2592028","url":null,"abstract":"NAND flash storage is widely adopted in all classes of computing devices. However, random write performance and lifetime issues remain to be addressed. In this paper, we propose a novel buffer replacement algorithm called TS-CLOCK that effectively resolves the remaining problems. Our experimental results show that TS-CLOCK outperforms state-of-the-art algorithms in terms of performance and lifetime.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126513198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a resource allocation problem in a multi-class server with convex holding costs and user impatience under the average cost criterion. In general, the optimal policy has a complex dependency on all the input parameters and state information. Our main contribution is to derive index policies that can serve as heuristics and are shown to give good performance. Our index policy attributes to each class an index, which depends on the number of customers currently present in that class. The index values are obtained by solving a relaxed version of the optimal stochastic control problem and combining results from restless multi-armed bandits and queueing theory. They can be expressed as a function of the steady-state distribution probabilities of a one-dimensional birth-and-death process. For linear holding cost, the index can be calculated in closed-form and turns out to be independent of the arrival rates and the number of customers present. In the case of no abandonments and linear holding cost, our index coincides with the cμ-rule, which is known to be optimal in this simple setting. For general convex holding cost we derive properties of the index value in limiting regimes: we consider the behavior of the index (i) as the number of customers in a class grows large, which allows us to derive the asymptotic structure of the index policies, and (ii) as the abandonment rate vanishes, which allows us to retrieve an index policy proposed for the multi-class M/M/1 queue with convex holding cost and no abandonments. In fact, in a multi-server environment it follows from recent advances that the index policy is asymptotically optimal for linear holding cost. To obtain further insights into the index policy, we consider the fluid version of the relaxed problem and derive a closed-form expression for the fluid index. The latter coincides with the stochastic model in case of linear holding costs. For arbitrary convex holding cost the fluid index can be seen as the Gcμθ-rule, that is, including abandonments into the generalized cμ-rule (Gcμ-rule). Numerical experiments show that our index policies become optimal as the load in the system increases.
{"title":"Index policies for a multi-class queue with convex holding cost and abandonments","authors":"M. Larrañaga, U. Ayesta, M. Verloop","doi":"10.1145/2591971.2591983","DOIUrl":"https://doi.org/10.1145/2591971.2591983","url":null,"abstract":"We investigate a resource allocation problem in a multi-class server with convex holding costs and user impatience under the average cost criterion. In general, the optimal policy has a complex dependency on all the input parameters and state information. Our main contribution is to derive index policies that can serve as heuristics and are shown to give good performance. Our index policy attributes to each class an index, which depends on the number of customers currently present in that class. The index values are obtained by solving a relaxed version of the optimal stochastic control problem and combining results from restless multi-armed bandits and queueing theory. They can be expressed as a function of the steady-state distribution probabilities of a one-dimensional birth-and-death process. For linear holding cost, the index can be calculated in closed-form and turns out to be independent of the arrival rates and the number of customers present. In the case of no abandonments and linear holding cost, our index coincides with the cμ-rule, which is known to be optimal in this simple setting. For general convex holding cost we derive properties of the index value in limiting regimes: we consider the behavior of the index (i) as the number of customers in a class grows large, which allows us to derive the asymptotic structure of the index policies, and (ii) as the abandonment rate vanishes, which allows us to retrieve an index policy proposed for the multi-class M/M/1 queue with convex holding cost and no abandonments. In fact, in a multi-server environment it follows from recent advances that the index policy is asymptotically optimal for linear holding cost. To obtain further insights into the index policy, we consider the fluid version of the relaxed problem and derive a closed-form expression for the fluid index. The latter coincides with the stochastic model in case of linear holding costs. For arbitrary convex holding cost the fluid index can be seen as the Gcμθ-rule, that is, including abandonments into the generalized cμ-rule (Gcμ-rule). Numerical experiments show that our index policies become optimal as the load in the system increases.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114188709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu Cai, Gulay Yalcin, O. Mutlu, E. Haratsch, O. Unsal, A. Cristal, K. Mai
Continued scaling of NAND flash memory to smaller process technology nodes decreases its reliability, necessitating more sophisticated mechanisms to correctly read stored data values. To distinguish between different potential stored values, conventional techniques to read data from flash memory employ a single set of reference voltage values, which are determined based on the overall threshold voltage distribution of flash cells. Unfortunately, the phenomenon of program interference, in which a cell's threshold voltage unintentionally changes when a neighboring cell is programmed, makes this conventional approach increasingly inaccurate in determining the values of cells. This paper makes the new empirical observation that identifying the value stored in the immediate-neighbor cell makes it easier to determine the data value stored in the cell that is being read. We provide a detailed statistical and experimental characterization of threshold voltage distribution of flash memory cells conditional upon the immediate-neighbor cell values, and show that such conditional distributions can be used to determine a set of read reference voltages that lead to error rates much lower than when a single set of reference voltage values based on the overall distribution are used. Based on our analyses, we propose a new method for correcting errors in a flash memory page, neighbor-cell assisted correction (NAC). The key idea is to re-read a flash memory page that fails error correction codes (ECC) with the set of read reference voltage values corresponding to the conditional threshold voltage distribution assuming a neighbor cell value and use the re-read values to correct the cells that have neighbors with that value. Our simulations show that NAC effectively improves flash memory lifetime by 33% while having no (at nominal lifetime) or very modest (less than 5% at extended lifetime) performance overhead.
{"title":"Neighbor-cell assisted error correction for MLC NAND flash memories","authors":"Yu Cai, Gulay Yalcin, O. Mutlu, E. Haratsch, O. Unsal, A. Cristal, K. Mai","doi":"10.1145/2591971.2591994","DOIUrl":"https://doi.org/10.1145/2591971.2591994","url":null,"abstract":"Continued scaling of NAND flash memory to smaller process technology nodes decreases its reliability, necessitating more sophisticated mechanisms to correctly read stored data values. To distinguish between different potential stored values, conventional techniques to read data from flash memory employ a single set of reference voltage values, which are determined based on the overall threshold voltage distribution of flash cells. Unfortunately, the phenomenon of program interference, in which a cell's threshold voltage unintentionally changes when a neighboring cell is programmed, makes this conventional approach increasingly inaccurate in determining the values of cells.\u0000 This paper makes the new empirical observation that identifying the value stored in the immediate-neighbor cell makes it easier to determine the data value stored in the cell that is being read. We provide a detailed statistical and experimental characterization of threshold voltage distribution of flash memory cells conditional upon the immediate-neighbor cell values, and show that such conditional distributions can be used to determine a set of read reference voltages that lead to error rates much lower than when a single set of reference voltage values based on the overall distribution are used. Based on our analyses, we propose a new method for correcting errors in a flash memory page, neighbor-cell assisted correction (NAC). The key idea is to re-read a flash memory page that fails error correction codes (ECC) with the set of read reference voltage values corresponding to the conditional threshold voltage distribution assuming a neighbor cell value and use the re-read values to correct the cells that have neighbors with that value. Our simulations show that NAC effectively improves flash memory lifetime by 33% while having no (at nominal lifetime) or very modest (less than 5% at extended lifetime) performance overhead.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114729954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weijie Shi, Linquan Zhang, Chuan Wu, Zongpeng Li, F. Lau
Auction mechanisms have recently attracted substantial attention as an efficient approach to pricing and resource allocation in cloud computing. This work, to the authors' knowledge, represents the first online combinatorial auction designed in the cloud computing paradigm, which is general and expressive enough to both (a) optimize system efficiency across the temporal domain instead of at an isolated time point, and (b) model dynamic provisioning of heterogeneous Virtual Machine (VM) types in practice. The final result is an online auction framework that is truthful, computationally efficient, and guarantees a competitive ratio ~ e+ 1 over e-1 ~ 3.30 in social welfare in typical scenarios. The framework consists of three main steps: (1) a tailored primal-dual algorithm that decomposes the long-term optimization into a series of independent one-shot optimization problems, with an additive loss of 1 over e-1 in competitive ratio, (2) a randomized auction sub-framework that applies primal-dual optimization for translating a centralized co-operative social welfare approximation algorithm into an auction mechanism, retaining a similar approximation ratio while adding truthfulness, and (3) a primal-dual update plus dual fitting algorithm for approximating the one-shot optimization with a ratio λ close to e. The efficacy of the online auction framework is validated through theoretical analysis and trace-driven simulation studies. We are also in the hope that the framework, as well as its three independent modules, can be instructive in auction design for other related problems.
{"title":"An online auction framework for dynamic resource provisioning in cloud computing","authors":"Weijie Shi, Linquan Zhang, Chuan Wu, Zongpeng Li, F. Lau","doi":"10.1145/2591971.2591980","DOIUrl":"https://doi.org/10.1145/2591971.2591980","url":null,"abstract":"Auction mechanisms have recently attracted substantial attention as an efficient approach to pricing and resource allocation in cloud computing. This work, to the authors' knowledge, represents the first online combinatorial auction designed in the cloud computing paradigm, which is general and expressive enough to both (a) optimize system efficiency across the temporal domain instead of at an isolated time point, and (b) model dynamic provisioning of heterogeneous Virtual Machine (VM) types in practice. The final result is an online auction framework that is truthful, computationally efficient, and guarantees a competitive ratio ~ e+ 1 over e-1 ~ 3.30 in social welfare in typical scenarios. The framework consists of three main steps: (1) a tailored primal-dual algorithm that decomposes the long-term optimization into a series of independent one-shot optimization problems, with an additive loss of 1 over e-1 in competitive ratio, (2) a randomized auction sub-framework that applies primal-dual optimization for translating a centralized co-operative social welfare approximation algorithm into an auction mechanism, retaining a similar approximation ratio while adding truthfulness, and (3) a primal-dual update plus dual fitting algorithm for approximating the one-shot optimization with a ratio λ close to e. The efficacy of the online auction framework is validated through theoretical analysis and trace-driven simulation studies. We are also in the hope that the framework, as well as its three independent modules, can be instructive in auction design for other related problems.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123965507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop two models of highway traffic: (i) a deterministic fluid model based on conservation laws building on previous work and (ii) a mean-field model of a series of infinite server queues, where each stage in the tandem models a segment of highway. The models define the ``highway-map''---a transformation of time-varying arrival rate functions according to which vehicles arrive at the highway to the corresponding departure rate functions of vehicles exiting the highway. The two models are shown to be equivalent in that they obtain the same highway-map. The cost of congestion for vehicles traversing the highway is the total extra time they spend on the highway due to congestion. This cost is shown to be equal to the ``d-bar'' distance between the input and the output rate measures of the highway-map. This fact is used to formulate a convex optimization problem for determining the optimal way to shift users from peak to off-peak hours using incentives so that congestion costs are lowered.
{"title":"Traffic congestion: models, costs and optimal transport","authors":"Chinmoy Mandayam, B. Prabhakar","doi":"10.1145/2591971.2592014","DOIUrl":"https://doi.org/10.1145/2591971.2592014","url":null,"abstract":"We develop two models of highway traffic: (i) a deterministic fluid model based on conservation laws building on previous work and (ii) a mean-field model of a series of infinite server queues, where each stage in the tandem models a segment of highway. The models define the ``highway-map''---a transformation of time-varying arrival rate functions according to which vehicles arrive at the highway to the corresponding departure rate functions of vehicles exiting the highway. The two models are shown to be equivalent in that they obtain the same highway-map. The cost of congestion for vehicles traversing the highway is the total extra time they spend on the highway due to congestion. This cost is shown to be equal to the ``d-bar'' distance between the input and the output rate measures of the highway-map. This fact is used to formulate a convex optimization problem for determining the optimal way to shift users from peak to off-peak hours using incentives so that congestion costs are lowered.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129122414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Retransmissions represent a primary failure recovery mech- anism on all layers of communication network architecture. Similarly, fair sharing, e.g. processor sharing (PS), is a widely accepted approach to resource allocation among mul- tiple users. Recent work has shown that retransmissions in failure-prone, e.g. wireless ad hoc, networks can cause heavy tails and long delays. In this paper, we discover a new phe- nomenon showing that PS-based scheduling induces com- plete instability in the presence of retransmissions, regard- less of how low the traffic load may be. This phenomenon occurs even when the job sizes are bounded/fragmented, e.g. deterministic. Our analytical results are further validated via simulation experiments. Moreover, our work demon- strates that scheduling one job at a time, such as first-come- first-serve, achieves stability and should be preferred in these systems.
{"title":"Is sharing with retransmissions causing instabilities?","authors":"P. Jelenkovic, E. Skiani","doi":"10.1145/2591971.2592001","DOIUrl":"https://doi.org/10.1145/2591971.2592001","url":null,"abstract":"Retransmissions represent a primary failure recovery mech- anism on all layers of communication network architecture. Similarly, fair sharing, e.g. processor sharing (PS), is a widely accepted approach to resource allocation among mul- tiple users. Recent work has shown that retransmissions in failure-prone, e.g. wireless ad hoc, networks can cause heavy tails and long delays. In this paper, we discover a new phe- nomenon showing that PS-based scheduling induces com- plete instability in the presence of retransmissions, regard- less of how low the traffic load may be. This phenomenon occurs even when the job sizes are bounded/fragmented, e.g. deterministic. Our analytical results are further validated via simulation experiments. Moreover, our work demon- strates that scheduling one job at a time, such as first-come- first-serve, achieves stability and should be preferred in these systems.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"350 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120883171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Caches play a critical role in today's computer systems and optimizing their performance has been a critical objective in the last couple of decades. Unfortunately, compared to a plethora of work in software and hardware directed code/data optimizations, much less effort has been spent in understanding the fundamental characteristics of data access patterns exhibited by application programs and their interaction with the underlying cache hardware. Therefore, in general it is hard to reason about cache behavior of a program running on a target system. Motivated by this observation, we first set up a "locality model" that can help us determine the theoretical bounds of the cache misses caused by irregular data accesses. We then explain how this locality model can be used for different data locality optimization purposes. After that, based on our model, we propose a data reordering (data layout reorganization) scheme that can be applied after any existing data reordering schemes for irregular applications to improve cache performance by further reducing the cache misses. We evaluate the effectiveness of our scheme using a set of 8 programs with irregular data accesses, and show that it brings significant improvements over the state-of-the-art on two commercial multicore machines.
{"title":"CApRI: CAche-conscious data reordering for irregular codes","authors":"W. Ding, M. Kandemir","doi":"10.1145/2591971.2591992","DOIUrl":"https://doi.org/10.1145/2591971.2591992","url":null,"abstract":"Caches play a critical role in today's computer systems and optimizing their performance has been a critical objective in the last couple of decades. Unfortunately, compared to a plethora of work in software and hardware directed code/data optimizations, much less effort has been spent in understanding the fundamental characteristics of data access patterns exhibited by application programs and their interaction with the underlying cache hardware. Therefore, in general it is hard to reason about cache behavior of a program running on a target system. Motivated by this observation, we first set up a \"locality model\" that can help us determine the theoretical bounds of the cache misses caused by irregular data accesses. We then explain how this locality model can be used for different data locality optimization purposes. After that, based on our model, we propose a data reordering (data layout reorganization) scheme that can be applied after any existing data reordering schemes for irregular applications to improve cache performance by further reducing the cache misses. We evaluate the effectiveness of our scheme using a set of 8 programs with irregular data accesses, and show that it brings significant improvements over the state-of-the-art on two commercial multicore machines.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121321987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Manish Arora, Srilatha Manne, Yasuko Eckert, Indrani Paul, N. Jayasena, D. Tullsen
Idle power is a significant contributor to overall energy consumption in modern multi-core processors. Cores can enter a full-sleep state, also known as C6, to reduce idle power; however, entering C6 incurs performance and power overheads. Since power gating can result in negative savings, hardware vendors implement various algorithms to manage C6 entry. In this paper, we examine state-of-the-art C6 entry algorithms and present a comparative analysis in the context of consumer and CPU-GPU benchmarks.
{"title":"A comparison of core power gating strategies implemented in modern hardware","authors":"Manish Arora, Srilatha Manne, Yasuko Eckert, Indrani Paul, N. Jayasena, D. Tullsen","doi":"10.1145/2591971.2592017","DOIUrl":"https://doi.org/10.1145/2591971.2592017","url":null,"abstract":"Idle power is a significant contributor to overall energy consumption in modern multi-core processors. Cores can enter a full-sleep state, also known as C6, to reduce idle power; however, entering C6 incurs performance and power overheads. Since power gating can result in negative savings, hardware vendors implement various algorithms to manage C6 entry. In this paper, we examine state-of-the-art C6 entry algorithms and present a comparative analysis in the context of consumer and CPU-GPU benchmarks.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116444342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Subhashini Krishnasamy, Siddhartha Banerjee, S. Shakkottai
We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint is motivated by modern social networks, wherein messages are broadcast to all neighbors, but attention spans are limited. Bounded susceptibility also arises in distributed computing applications with download bandwidth constraints, and in human epidemics under quarantine policies. Network epidemics have been extensively studied in literature; prior work characterizes the graph structures required to ensure fast spreading under the SI dynamics, and long lifetime under the SIS dynamics. In particular, these conditions turn out to be meaningful for two classes of networks of practical relevance -- dense, uniform (i.e., clique-like) graphs, and sparse, structured (i.e., star-like) graphs. We show that bounded susceptibility has a surprising impact on epidemic behavior in these graph families. For the SI dynamics, bounded susceptibility has no effect on star-like networks, but dramatically alters the spreading time in clique-like networks. In contrast, for the SIS dynamics, clique-like networks are unaffected, but star-like networks exhibit a sharp change in extinction times under bounded susceptibility. Our findings are useful for the design of disease-resistant networks and infrastructure networks. More generally, they show that results for existing epidemic models are sensitive to modeling assumptions in non-intuitive ways, and suggest caution in directly using these as guidelines for real systems.
{"title":"The behavior of epidemics under bounded susceptibility","authors":"Subhashini Krishnasamy, Siddhartha Banerjee, S. Shakkottai","doi":"10.1145/2591971.2591977","DOIUrl":"https://doi.org/10.1145/2591971.2591977","url":null,"abstract":"We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint is motivated by modern social networks, wherein messages are broadcast to all neighbors, but attention spans are limited. Bounded susceptibility also arises in distributed computing applications with download bandwidth constraints, and in human epidemics under quarantine policies.\u0000 Network epidemics have been extensively studied in literature; prior work characterizes the graph structures required to ensure fast spreading under the SI dynamics, and long lifetime under the SIS dynamics. In particular, these conditions turn out to be meaningful for two classes of networks of practical relevance -- dense, uniform (i.e., clique-like) graphs, and sparse, structured (i.e., star-like) graphs. We show that bounded susceptibility has a surprising impact on epidemic behavior in these graph families. For the SI dynamics, bounded susceptibility has no effect on star-like networks, but dramatically alters the spreading time in clique-like networks. In contrast, for the SIS dynamics, clique-like networks are unaffected, but star-like networks exhibit a sharp change in extinction times under bounded susceptibility.\u0000 Our findings are useful for the design of disease-resistant networks and infrastructure networks. More generally, they show that results for existing epidemic models are sensitive to modeling assumptions in non-intuitive ways, and suggest caution in directly using these as guidelines for real systems.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"385 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115221692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider randomized job routing techniques for a system consisting of a large number of parallel processor sharing servers with heterogeneous server speeds. In particular, a scheme, that routes an incoming job request to the server providing the highest instantaneous processing rate per job among two servers, chosen uniformly at random, is proposed. We show that, unlike the homogeneous case, in the heterogeneous case, such randomized dynamic schemes need not always perform better than the optimal static scheme (in which jobs are assigned to servers with fixed probabilities independent of server states) in terms of reducing the mean response time of jobs. Specifically, we show that the stability region under the proposed scheme is a subset of that under the optimal static routing scheme. We also obtain the stationary tail distribution of server occupancies for the proposed scheme in the limit as the system size grows to infinity. This distribution has been shown to be insensitive to job length distribution and decay super-exponentially.
{"title":"Randomized routing schemes for large processor sharing systems with multiple service rates","authors":"Arpan Mukhopadhyay, R. Mazumdar","doi":"10.1145/2591971.2592015","DOIUrl":"https://doi.org/10.1145/2591971.2592015","url":null,"abstract":"We consider randomized job routing techniques for a system consisting of a large number of parallel processor sharing servers with heterogeneous server speeds. In particular, a scheme, that routes an incoming job request to the server providing the highest instantaneous processing rate per job among two servers, chosen uniformly at random, is proposed. We show that, unlike the homogeneous case, in the heterogeneous case, such randomized dynamic schemes need not always perform better than the optimal static scheme (in which jobs are assigned to servers with fixed probabilities independent of server states) in terms of reducing the mean response time of jobs. Specifically, we show that the stability region under the proposed scheme is a subset of that under the optimal static routing scheme. We also obtain the stationary tail distribution of server occupancies for the proposed scheme in the limit as the system size grows to infinity. This distribution has been shown to be insensitive to job length distribution and decay super-exponentially.","PeriodicalId":306456,"journal":{"name":"Measurement and Modeling of Computer Systems","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123824895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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