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15 Sep 2011: Denote by F, = F ( N n r B n , c n ) the current fraction of cells lost a t buffer n, for all buffers n in the network. ... Under these assumptions, D will have a negligible dependence on B as well (for large B ). Consequently, the probability t h a t

15 Sep 2011: Thus the. expected wasted space is bounded by some B for all t. ... Thus the wasted space satisfies I B' I|1/N < Wt' | I B' I|1N for all possible packings.

31 Oct 2011: From the above, the minimum subsidy that makes (1, 1)passive also makes all states passive. ... 1. We shallprove by induction on s that that for all valid state vectors(ω̄1, y, ω̄2, ω̄3).

15 Sep 2011: Note that not all n customers will choose a dynamic contract, butwe will address this issue later on. ... of band-width, while with probability 1pi he does not buy nothing at all, with pi beinguniform in [0, a/b].

15 Sep 2011: Mtisfies (b) for all StMM with a 111-ponent of value k or bigger by (2.2) and the fact that M isk-liiited. ... The newfunction has all positive coefficients and will continue tosatisfy (b) with y replaced by y/2 >0.

15 Sep 2011: manner until all machines are assigned or all jobs are allocated to machines. ... The uniform, exponential, hyperex- ponential, gamma, and folded-normal distributions all have sc2 densities.

15 Sep 2011: 1, 0, 2).Let PS,b denote the set of all perfect packing configurations for a given S and b. ... LetΛS,b be the convex cone in Rd spanned by all nonnegative linear combinations ofconfigurations in PS,b.

15 Sep 2011: Then 7r minimizes E[ J', cj Uj] amongst all the static list policies. ... All the jobs are present at time 0, so T7 = SJ Qr ,dt.

15 Sep 2011: b) The worst possible growth rate for expected waste. of FFD over all pairs j,k is n1624 = (.00160. ) ... 1,0,2). Let P,B denote the set of all perfect packing. configurations for a given S and B.

15 Sep 2011: Only the first two customers purchasecontracts. If we have wanted to ensure that all three customers. ... An important question thatmay rise is how the shape of the utility function affects all theaforementioned results.

31 Oct 2011: simultaneously. The parametersof the contracts become finalized once all agents have madetheir bids. ... post ones, eitherfor C3, or for C1 and C2, but not for all.

15 Sep 2011: This distribution is known to all agents, butthe value of is known to agent alone. ... this denotes all the preferences parameters apart from. Theproblem is to maximize expected social welfare.

15 Sep 2011: terms of maintaining guaranteedservice to all customers) as two units of service A. ... This is the charging method which is adopted by an all-you-can-eat restaurant.

15 Sep 2011: Place the next item so as to minimize P1i<B n(g)2.For all the discrete distributions we have tested, SS appears to produce sublinearexpected waste whenever the optimal expected ... assume that all discrete distributions have beenscaled up by an

15 Sep 2011: If there is a function V : Z [1, ),constants b < , β > 0, and a finite subset C Z such that for all x Z,. ... that (a) sS µ(s) = 1 and (b) for all states s′ S,µ(s′) =. sS µ(s)ps(s. ′). If we let sn denote the state after n steps, then

15 Sep 2011: there exists a bin-packing algorithm whose use guarantees the expected wasted space is less than B for all t. ... Thus the expected wasted space is bounded by some B for all t.

15 Sep 2011: All the services are deter- ministic, with a duration of 1 time unit. ... It can now be shown that the whole expression is maximized over the range -a < b - a by b = 0 for all 0 < a < 1/2.

15 Sep 2011: We define a system to be stabilizable if, for any arrivalprocess in L{), a policy exists under which E[xt(t)] < B < <x> for all times t.A system is/-stabilizable ... When a bin is filled with all the type a items itcan store, it is immediately filled

15 Sep 2011: By m o v i n g a j o b all the w a y a r o u n d the cycle, f r o m n o d ... All these decisions are to be m a d e dynamically as a function of the n u m b e r o f jobs.

15 Sep 2011: a) [Initial Bound Hypothesis]. E[bφ(X1). ]<. (b) [Bounded Variation Hypothesis]. For all N 1, |φ(XN1)φ(XN)|. ... tation. The state space S is the set of all length-(B 1) vectors of non-negativeintegers x̄= 〈x1,x2,.