3 research outputs found
Self-Learning Threshold-Based Load Balancing
We consider a large-scale service system where incoming tasks have to be
instantaneously dispatched to one out of many parallel server pools. The
user-perceived performance degrades with the number of concurrent tasks and the
dispatcher aims at maximizing the overall quality-of-service by balancing the
load through a simple threshold policy. We demonstrate that such a policy is
optimal on the fluid and diffusion scales, while only involving a small
communication overhead, which is crucial for large-scale deployments. In order
to set the threshold optimally, it is important, however, to learn the load of
the system, which may be unknown. For that purpose, we design a control rule
for tuning the threshold in an online manner. We derive conditions which
guarantee that this adaptive threshold settles at the optimal value, along with
estimates for the time until this happens. In addition, we provide numerical
experiments which support the theoretical results and further indicate that our
policy copes effectively with time-varying demand patterns.Comment: 51 pages, 6 figure
Pass-and-Swap Queues
Order-independent (OI) queues, introduced by Berezner, Kriel, and Krzesinski
in 1995, expanded the family of multi-class queues that are known to have a
product-form stationary distribution by allowing for intricate class-dependent
service rates. This paper further broadens this family by introducing
pass-and-swap (P&S) queues, an extension of OI queues where, upon a service
completion, the customer that completes service is not necessarily the one that
leaves the system. More precisely, we supplement the OI queue model with an
undirected graph on the customer classes, which we call a swapping graph, such
that there is an edge between two classes if customers of these classes can be
swapped with one another. When a customer completes service, it passes over
customers in the remainder of the queue until it finds a customer it can swap
positions with, that is, a customer whose class is a neighbor in the graph. In
its turn, the customer that is ejected from its position takes the position of
the next customer it can be swapped with, and so on. This is repeated until a
customer can no longer find another customer to be swapped with; this customer
is the one that leaves the queue. After proving that P&S queues have a
product-form stationary distribution, we derive a necessary and sufficient
stability condition for (open networks of) P&S queues that also applies to OI
queues. We then study irreducibility properties of closed networks of P&S
queues and derive the corresponding product-form stationary distribution.
Lastly, we demonstrate that closed networks of P&S queues can be applied to
describe the dynamics of new and existing load-distribution and scheduling
protocols in clusters of machines in which jobs have assignment constraints.Comment: 44 pages, 15 figure