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Higher response time moments for M/M/1 discriminatory processor sharing queues

Tiberiu Chis, Peter Harrison
2016 Proceedings of the 9th EAI International Conference on Performance Evaluation Methodologies and Tools  
Response time; M/M/1; discriminatory processor sharing VALUETOOLS 2015,  ...  Hence, we build an automated numerical algorithm for calculating higher moments of response time in M/M/1-DPS queues for multiple job classes and test two different case studies.  ...  formula for the third moment of response time in M/M/1-DPS queues for two classes. • Obtain arbitrary (up to any order) response time moments numerically for multi-class M/M/1-DPS queues.  ... 
doi:10.4108/eai.14-12-2015.2262730 dblp:journals/sis/ChisH16 fatcat:ewt73qx2vrfatmz7o7zbord6hi

A survey on discriminatory processor sharing

Eitan Altman, Konstantin Avrachenkov, Urtzi Ayesta
2006 Queueing systems  
The Discriminatory Processor Sharing (DPS) model is a multi-class generalization of the egalitarian Processor Sharing model.  ...  The present article provides an overview of the analytical results for the DPS model. In particular, we focus on response times and numbers of jobs in the system.  ...  Acknowledgments The authors wish to thank the anonymous reviewers for the careful reading and for providing valuable comments that helped improve the presentation.  ... 
doi:10.1007/s11134-006-7586-8 fatcat:sv6qollf5naurnamre7ouancwy

Performance modelling with adaptive hidden Markov models and discriminatory processor sharing queues

Tiberiu Chis, Peter Harrison, Engineering And Physical Sciences Research Council
2016
Therefore, we propose a class of discrete, processor-sharing queues for approximating queueing delay as response time distributions, which represent service level agreements at specific spatiotemporal  ...  We adapt discrete queues to model job arrivals with distributions given by a Markov-modulated Poisson process (MMPP) and served under discriminatory processor-sharing scheduling.  ...  Response time approximation For M/M/1-EPS and M/M/1-DPS queues (i.e. discrete queues with egalitarian and discriminatory processor-sharing disciplines, respectively), we approximate response time moments  ... 
doi:10.25560/39049 fatcat:3xlsn67xcvfclgmn3vpnu2y7aa

Moment-Generating Algorithm for Response Time in Processor Sharing Queueing Systems [chapter]

Tiberiu Chis, Peter Harrison
2015 Lecture Notes in Computer Science  
A new moment-generating algorithm for calculating response times analytically is obtained, based on M/M/1 processor sharing (PS) queueing models.  ...  This algorithm is compared against existing work on response times in M/M/1-PS queues and extended to M/M/1 discriminatory PS queues. Two real-world case studies are evaluated. 1.  ...  Related work on response times There are a number of works on approximating response time under PS scheduling, but few which adopt analytical queueing theory, even for the Markovian M/M/1-PS queue.  ... 
doi:10.1007/978-3-319-23267-6_6 fatcat:neh7lxhu7bdi5jy7di2tnhybla

Violation Probability in Processor-Sharing Queues

Na Chen, Scott Jordan
2008 IEEE Transactions on Automatic Control  
For an M/G/l processor-sharing queue, we give a closed-form expression for this violation probability.  ...  For an M/G/1 processor-sharing queue, we give a closed-form expression for this violation probability.  ...  There is a rich literature concerning processor-sharing queues and discriminatory processor-sharing (DPS) queues. The most important performance metric for such queues is sojourn time.  ... 
doi:10.1109/tac.2008.929875 fatcat:cjxhzz3m65cepgj7yngf2abe4e

Processor Sharing Queueing Models of Mixed Scheduling Disciplines for Time Shared System

L. Kleinrock, R. R. Muntz
1972 Journal of the ACM  
Scheduling algorithms for time shared computing facilities are considered in terms of a queueing theory model.  ...  The average response time for jobs conditioned on their service requirement is solved for.  ...  Besides originally suggesting the fruitful approach of treating each line as an M/M/1 queue, Dr.  ... 
doi:10.1145/321707.321717 fatcat:lfdzj6agmvff5lik6hv74nicd4

Heavy Traffic Approximation of Equilibria in Resource Sharing Games

Yu Wu, Loc Bui, Ramesh Johari
2012 IEEE Journal on Selected Areas in Communications  
We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior.  ...  We discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium.  ...  (This follows because the discriminatory processor sharing policy is work-conserving, so the length of a busy period will be identical to that in an M/M/1 queue.)  ... 
doi:10.1109/jsac.2012.121212 fatcat:j5ohysqyq5cu5bfpgxwtyaltfq

Heavy Traffic Approximation of Equilibria in Resource Sharing Games [chapter]

Yu Wu, Loc Bui, Ramesh Johari
2011 Lecture Notes in Computer Science  
We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior.  ...  We discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium.  ...  (This follows because the discriminatory processor sharing policy is work-conserving, so the length of a busy period will be identical to that in an M/M/1 queue.)  ... 
doi:10.1007/978-3-642-25510-6_30 fatcat:ungcsm5kd5crjnwmiw7ouoi2ey

A diffusion model for two parallel queues with processor sharing: transient behavior and asymptotics

Charles Knessl
1999 Journal of Applied Mathematics and Stochastic Analysis  
We consider two identical, parallel M/M/1 queues. Both queues are fed by a Poisson arrival stream of rate I and have service rates equal to #.  ...  This is called head-@the-line processor sharing. We study this model in the heavy traffic limit, where p 1/#1.  ...  Diffusion Model for Two Parallel Queues 337 Acknowledgement would like to thank the referee(s) for their very useful suggestions.  ... 
doi:10.1155/s1048953399000295 fatcat:fmixb2737bhvfgfba2s4j6hjiu

Sojourn time asymptotics in processor-sharing queues

Sem Borst, Rudesindo Núñez-Queija, Bert Zwart
2006 Queueing systems  
Over the past few decades, the Processor-Sharing (PS) discipline has attracted a great deal of attention in the queueing literature.  ...  In contrast to the simple geometric queue length distribution, the sojourn time lacks such a nice closed-form characterization, even for exponential service requirements.  ...  versions such as Discriminatory Processor Sharing queues; (iii) renewal arrival processes.  ... 
doi:10.1007/s11134-006-7585-9 fatcat:fugrba5pvvho5meoepsx2mhn7a

Heavy Traffic Approximation of Equilibria in Resource Sharing Games [article]

Yu Wu, Loc Bui, Ramesh Johari
2012 arXiv   pre-print
We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior.  ...  We discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium.  ...  (This follows because the discriminatory processor sharing policy is work-conserving, so the length of a busy period will be identical to that in an M/M/1 queue.)  ... 
arXiv:1109.6166v3 fatcat:xelohfdg6bhtlbxp7a75hkwjla

Towards more effective utilization of computer systems

Niklas Carlsson, Martin Arlitt
2011 Proceeding of the second joint WOSP/SIPEW international conference on Performance engineering - ICPE '11  
Much of this infrastructure is under utilized to ensure acceptable response times. This results in less than ideal use of the capital investment used to purchase the IT equipment.  ...  Our results show that computer systems running delay-sensitive (e.g., Web) workloads can be more effectively utilized while still maintaining adequate (e.g., mean or upper percentile) response times.  ...  [3] use an M/M/m queue (rather than multiple independent M/M/1 queues) to show the utilization improvements using multi-socket systems. We will explore more advanced models in future work.  ... 
doi:10.1145/1958746.1958781 dblp:conf/wosp/CarlssonA11 fatcat:rcbgiqnpw5h6ha66o4fkjktbrm

Optimal resource allocation in synchronized multi-tier Internet services

Chrétien Verhoef, Sandjai Bhulai, Rob van der Mei
2011 Performance evaluation (Print)  
For these systems, providing good response time performance is crucial for the commercial success.  ...  In practice, the response-time performance of multi-tiered systems is often degraded by severe synchronization problems, causing jobs to wait for responses from different tiers.  ...  Results for the business logic, modeled as a processor sharing (PS) node, are given in [6] , where the Laplace-Stieltjes Transform (LST) is obtained for the M/M/1/PS node.  ... 
doi:10.1016/j.peva.2011.07.020 fatcat:kswgg4wgq5fybgpuj2kv5u752q

Pigouvian Tolls and Welfare Optimality with Parallel Servers and Heterogeneous Customers [article]

Tejas Bodas, A. Ganesh, D. Manjunath
2021 arXiv   pre-print
Optimization by self-interested agents in such settings typically results in equilibria which are sub-optimal for social welfare.  ...  Pigouvian taxes or tolls, which impose a user charge equal to the negative externality caused by the marginal user to other users, are a mechanism for combating this problem.  ...  Bodas and Manjunath acknowledge support from the Bharti Centre for Communication at IIT Bombay, CEFIPRA and IFCAM.  ... 
arXiv:1409.7195v4 fatcat:plbssfyabjehrevv6rij4onsnu

Stability of size-based scheduling disciplines in resource-sharing networks

Maaike Verloop, Sem Borst, Rudesindo Núñez-Queija
2005 Performance evaluation (Print)  
Since class-i users for i = 1, . . . , L, always receive priority over class-0 users, they behave as in an isolated M/M/1 queue with class i only.  ...  The Discriminatory Processor Sharing (DPS) discipline offers a more flexible instrument for accomplishing service differentiation [21] .  ... 
doi:10.1016/j.peva.2005.07.008 fatcat:anfn4lth5jfzbbcvu5iuuzjuyu
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