On the Complexity of Load Balancing in Dynamic Networks

Utility Maximizing Load Balancing Policies

“…In Section 6.4 we show that v n ⇒ 0 as n → ∞ with respect to a suitable topology. Informally, this implies that the asymptotic behavior of q n is essentially captured by (19) in the limit as n → ∞. Then we prove in Section 6.5 that {q n : n ≥ 1} is tight in D 1 [0, ∞).…”

“…The right-hand side of ( 29) is a measurable function of (N a k , R k , q k , v k ); see Appendix B for more details. This implies that the probability that (29) holds only depends on the law of (N a k , R k , q k , v k ), thus (29) holds with probability one in (Ω, F, P) by ( 17) and (19).…”

“…The problem of balancing a fixed workload across the nodes of a static network was first studied in [12], and the situation where the graph is dynamic was first considered in [2,13]; for a more extensive list of references see [19]. Most of this literature not only assumes that the workload is fixed but also that the graph or the sequence of graphs that describes the network is deterministic or adversarial.…”

“…Finally, ( 19) is used to establish that the limit q of any convergent subsequence satisfies (4) almost surely. Essentially, the first two terms of ( 19) yield the first term of (4) and the last term of (19) gives the last term of (4).…”

Online Job Scheduling with <i>K</i> Servers

“…For example, Konrad et al [12] combined the semi-matching with the streaming model in order to distribute data to multiple computers. Besides, Zhao et al [13], and Gilbert et al [14] used it to solve the resource allocation problems.…”