393 research outputs found
Selfish traffic allocation for server farms
We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price of selfish routing using the price of anarchy (a.k.a. the coordination ratio) and other (e.g., bicriteria) measures in the recently introduced game theoretic parallel links network model of Koutsoupias and Papadimitriou. We generalize this model toward general, monotone families of cost functions and cost functions from queueing theory. A summary of our main results for general, monotone cost functions is as follows: 1. We give an exact characterization of all cost functions having a bounded/unbounded price of anarchy. For example, the price of anarchy for cost functions describing the expected delay in queueing systems is unbounded. 2. We show that an unbounded price of anarchy implies an extremely high performance degradation under bicriteria measures. In fact, the price of selfish routing can be as high as a bandwidth degradation by a factor that is linear in the network size. 3. We separate the game theoretic (integral) allocation model from the (fractional) flow model by demonstrating that even a very small or negligible amount of integrality can lead to a dramatic performance degradation. 4. We unify recent results on selfish routing under different objectives by showing that an unbounded price of anarchy under the min-max objective implies an unbounded price of anarchy under the average cost objective and vice versa. Our special focus lies on cost functions describing the behavior of Web servers that can open only a limited number of Transmission Control Protocol (TCP) connections. In particular, we compare the performance of queueing systems that serve all incoming requests with servers that reject requests in case of overload. Our analysis indicates that all queueing systems without rejection cannot give any reasonable guarantee on the expected delay of requests under selfish routing even when the injected load is far away from the capacity of the system. In contrast, Web server farms that are allowed to reject requests can guarantee a high quality of service for every individual request stream even under relatively high injection rates
Multiclass multiserver queueing system in the Halfin-Whitt heavy traffic regime. Asymptotics of the stationary distribution
We consider a heterogeneous queueing system consisting of one large pool of
identical servers, where is the scaling parameter. The
arriving customers belong to one of several classes which determines the
service times in the distributional sense. The system is heavily loaded in the
Halfin-Whitt sense, namely the nominal utilization is where
is the spare capacity parameter. Our goal is to obtain bounds on the
steady state performance metrics such as the number of customers waiting in the
queue . While there is a rich literature on deriving process level
(transient) scaling limits for such systems, the results for steady state are
primarily limited to the single class case.
This paper is the first one to address the case of heterogeneity in the
steady state regime. Moreover, our results hold for any service policy which
does not admit server idling when there are customers waiting in the queue. We
assume that the interarrival and service times have exponential distribution,
and that customers of each class may abandon while waiting in the queue at a
certain rate (which may be zero). We obtain upper bounds of the form
on both and the number of idle servers. The bounds
are uniform w.r.t. parameter and the service policy. In particular, we show
that . Therefore, the
sequence is tight and has a uniform exponential tail
bound. We further consider the system with strictly positive abandonment rates,
and show that in this case every weak limit of
has a sub-Gaussian tail. Namely .Comment: 21 page
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