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  • 1
    Online Resource
    Online Resource
    Analysis of an Offloading Scheme for Data Centers in the Framework of Fog Computing
    Association for Computing Machinery (ACM) ; 2016
    In:  ACM Transactions on Modeling and Performance Evaluation of Computing Systems Vol. 1, No. 4 ( 2016-09-21), p. 1-18
    Details
    In: ACM Transactions on Modeling and Performance Evaluation of Computing Systems, Association for Computing Machinery (ACM), Vol. 1, No. 4 ( 2016-09-21), p. 1-18
    Abstract: In the context of fog computing, we consider a simple case where data centers are installed at the edge of the network and assume that if a request arrives at an overloaded data center, then it is forwarded to a neighboring data center with some probability. Data centers are assumed to have a large number of servers, and traffic at some of them is assumed to cause saturation. In this case, the other data centers may help to cope with this saturation regime by accepting some of the rejected requests. Our aim is to qualitatively estimate the gain achieved via cooperation between neighboring data centers. After proving some convergence results related to the scaling limits of loss systems for the process describing the number of free servers at both data centers, we show that the performance of the system can be expressed in terms of the invariant distribution of a random walk in the quarter plane. By using and developing existing results in the technical literature, explicit formulas for the blocking rates of such a system are derived.
    Type of Medium: Online Resource
    ISSN: 2376-3639 , 2376-3647
    URL: Article
    DOI: 10.1145/2950047
    Language: English
    Publisher: Association for Computing Machinery (ACM)
    Publication Date: 2016
    detail.hit.zdb_id: 2849372-2
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  • 2
    Online Resource
    Online Resource
    AN IDENTIFICATION PROBLEM IN AN URN AND BALL MODEL WITH HEAVY TAILED DISTRIBUTIONS
    Cambridge University Press (CUP) ; 2010
    In:  Probability in the Engineering and Informational Sciences Vol. 24, No. 1 ( 2010-01), p. 77-97
    Details
    In: Probability in the Engineering and Informational Sciences, Cambridge University Press (CUP), Vol. 24, No. 1 ( 2010-01), p. 77-97
    Abstract: We consider in this article an urn and ball problem with replacement, where balls are with different colors and are drawn uniformly from a unique urn. The numbers of balls with a given color are independent and identically distributed random variables with a heavy tailed probability distribution—for instance a Pareto or a Weibull distribution. We draw a small fraction p ≪1 of the total number of balls. The basic problem addressed in this article is to know to which extent we can infer the total number of colors and the distribution of the number of balls with a given color. By means of Le Cam's inequality and the Chen–Stein method, bounds for the total variation norm between the distribution of the number of balls drawn with a given color and the Poisson distribution with the same mean are obtained. We then show that the distribution of the number of balls drawn with a given color has the same tail as that of the original number of balls. Finally, we establish explicit bounds between the two distributions when each ball is drawn with fixed probability p .
    Type of Medium: Online Resource
    ISSN: 0269-9648 , 1469-8951
    URL: Article
    DOI: 10.1017/S0269964809990143
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2010
    detail.hit.zdb_id: 2010880-1
    SSG: 24,1
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  • 3
    Online Resource
    Online Resource
    Allocation schemes of resources with downgrading
    Cambridge University Press (CUP) ; 2017
    In:  Advances in Applied Probability Vol. 49, No. 2 ( 2017-06), p. 629-651
    Details
    In: Advances in Applied Probability, Cambridge University Press (CUP), Vol. 49, No. 2 ( 2017-06), p. 629-651
    Abstract: We consider a server with large capacity delivering video files encoded in various resolutions. We assume that the system is under saturation in the sense that the total demand exceeds the server capacity C . In such a case, requests may be rejected. For the policies considered in this paper, instead of rejecting a video request, it is downgraded. When the occupancy of the server is above some value C 0 〈 C , the server delivers the video at a minimal bit rate. The quantity C 0 is the bit rate adaptation threshold. For these policies, request blocking is thus replaced with bit rate adaptation. Under the assumptions of Poisson request arrivals and exponential service times, we show that, by rescaling the system, a process associated with the occupancy of the server converges to some limiting process whose invariant distribution is computed explicitly. This allows us to derive an asymptotic expression of the key performance measure of such a policy, namely the equilibrium probability that a request is transmitted at requested bitrate. Numerical applications of these results are presented.
    Type of Medium: Online Resource
    ISSN: 0001-8678 , 1475-6064
    URL: Article
    DOI: 10.1017/apr.2017.15
    RVK:
    SA 1600
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2017
    detail.hit.zdb_id: 1474602-5
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  • 4
    Online Resource
    Online Resource
    Perturbation analysis of a variable M/M/1 queue: a probabilistic approach
    Cambridge University Press (CUP) ; 2006
    In:  Advances in Applied Probability Vol. 38, No. 01 ( 2006-03), p. 263-283
    Details
    In: Advances in Applied Probability, Cambridge University Press (CUP), Vol. 38, No. 01 ( 2006-03), p. 263-283
    Abstract: In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process ( X ( t )) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process ( X ( t )) play a key role.
    Type of Medium: Online Resource
    ISSN: 0001-8678 , 1475-6064
    URL: Article
    DOI: 10.1017/S0001867800000902
    RVK:
    SA 1600
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2006
    detail.hit.zdb_id: 1474602-5
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  • 5
    Online Resource
    Online Resource
    Inference of flow statistics via packet sampling in the internet
    Institute of Electrical and Electronics Engineers (IEEE) ; 2008
    In:  IEEE Communications Letters Vol. 12, No. 12 ( 2008-12), p. 897-899
    Details
    In: IEEE Communications Letters, Institute of Electrical and Electronics Engineers (IEEE), Vol. 12, No. 12 ( 2008-12), p. 897-899
    Type of Medium: Online Resource
    ISSN: 1089-7798
    URL: Article
    DOI: 10.1109/LCOMM.2008.081124
    Language: Unknown
    Publisher: Institute of Electrical and Electronics Engineers (IEEE)
    Publication Date: 2008
    detail.hit.zdb_id: 2029374-4
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  • 6
    Online Resource
    Online Resource
    On the statistical characterization of flows in Internet traffic with application to sampling
    Elsevier BV ; 2010
    In:  Computer Communications Vol. 33, No. 1 ( 2010-1), p. 103-112
    Details
    In: Computer Communications, Elsevier BV, Vol. 33, No. 1 ( 2010-1), p. 103-112
    Type of Medium: Online Resource
    ISSN: 0140-3664
    URL: Article
    DOI: 10.1016/j.comcom.2009.08.006
    Language: English
    Publisher: Elsevier BV
    Publication Date: 2010
    detail.hit.zdb_id: 1478742-8
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  • 7
    Online Resource
    Online Resource
    Perturbation analysis of an M/M/1 queue in a diffusion random environment
    Springer Science and Business Media LLC ; 2009
    In:  Queueing Systems Vol. 61, No. 1 ( 2009-1), p. 1-35
    Details
    In: Queueing Systems, Springer Science and Business Media LLC, Vol. 61, No. 1 ( 2009-1), p. 1-35
    Type of Medium: Online Resource
    ISSN: 0257-0130 , 1572-9443
    URL: Article
    DOI: 10.1007/s11134-008-9098-1
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2009
    detail.hit.zdb_id: 2014596-2
    SSG: 11
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  • 8
    Online Resource
    Online Resource
    Analysis of Downgrading for Resource Allocation
    Association for Computing Machinery (ACM) ; 2016
    In:  ACM SIGMETRICS Performance Evaluation Review Vol. 44, No. 2 ( 2016-09-29), p. 24-26
    Details
    In: ACM SIGMETRICS Performance Evaluation Review, Association for Computing Machinery (ACM), Vol. 44, No. 2 ( 2016-09-29), p. 24-26
    Type of Medium: Online Resource
    ISSN: 0163-5999
    URL: Article
    DOI: 10.1145/3003977.3003986
    Language: English
    Publisher: Association for Computing Machinery (ACM)
    Publication Date: 2016
    detail.hit.zdb_id: 199353-7
    detail.hit.zdb_id: 2089001-1
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  • 9
    Online Resource
    Online Resource
    Perturbation analysis of a variable M/M/1 queue: a probabilistic approach
    Cambridge University Press (CUP) ; 2006
    In:  Advances in Applied Probability Vol. 38, No. 1 ( 2006-03), p. 263-283
    Details
    In: Advances in Applied Probability, Cambridge University Press (CUP), Vol. 38, No. 1 ( 2006-03), p. 263-283
    Abstract: In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process ( X ( t )) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process ( X ( t )) play a key role.
    Type of Medium: Online Resource
    ISSN: 0001-8678 , 1475-6064
    URL: Article
    DOI: 10.1239/aap/1143936150
    RVK:
    SA 1600
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2006
    detail.hit.zdb_id: 1474602-5
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