Concave function

Abstract: This paper investigates the joint user association (UA) and user scheduling (US) for load balancing in a wireless downlink heterogeneous network by formulating a network-wide utility maximization problem. In order to efficiently solve the problem, we first approximate the original non-convex throughput function to a concave function, and demonstrate that the gap for such approximation approaches zero when the number of users is sufficiently large. Then, a distributed algorithm is further proposed to obtain the UA and US solutions by exploiting the convex optimization technique known as alternating direction method of multipliers. A remarkable feature of the proposed algorithm is that apart from load balancing, multiuser diversity is exploited in the association time to further improve system performance. The simulation results show the superior performance of the proposed algorithm and underscore the significant benefits of jointly exploiting multiuser diversity and load balancing.

Abstract: Given a sequence A of length M and a regular expression R of length P, an approximate regular expression pattern matching algorithm computes the score of the best alignment between A and one of the sequences exactly matched by R There are a variety of schemes for scoring alignments In a concave gap-penalty scoring scheme, a function δ(a, b) gives the score of each aligned pair of symbols a and b, and a concave function w(k) gives the score of a sequence of unaligned symbols, or gap, of length k A function w is concave if and only if it has the property that for all k > 1, w(k+ 1)-w(k)

Abstract: This paper suggests that introducing randomization in queue discipline might be welfare enhancing in certain queues for which the cost of waiting is a concave function of waiting time. Concavity can make increased variability in waiting times good not bad for aggregate customer welfare. Such concavity may occur if the costs of waiting asymptotically approach some maximum or if the customer incurs a fixed cost if there is any wait at all. As examples, cost might asymptotically approach a maximum for patients seeking organ transplants who will not live beyond a certain threshold time, and fixed costs could pertain for knowledge workers seeking a piece of information that is required to proceed with their current task, so any delay creates a “set up charge” associated with switching tasks.