Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tightness of invariant distributions of a large-scale flexible service
  system under a priority discipline   We consider large-scale service systems with multiple customer classes and
multiple server pools; interarrival and service times are exponentially
distributed, and mean service times depend both on the customer class and
server pool. It is assumed that the allowed activities (routing choices) form a
tree (in the graph with vertices being both customer classes and server pools).
We study the behavior of the system under a Leaf Activity Priority (LAP)
policy, which assigns static priorities to the activities in the order of
sequential "elimination" of the tree leaves.
  We consider the scaling limit of the system as the arrival rate of customers
and number of servers in each pool tend to infinity in proportion to a scaling
parameter r, while the overall system load remains strictly subcritical.
Indexing the systems by parameter r, we show that (a) the system under LAP
discipline is stochastically stable for all sufficiently large r and (b) the
family of the invariant distributions is tight on scales $r^{1/2 + \epsilon}$
for all $\epsilon > 0$. (More precisely, the sequence of invariant
distributions, centered at the equilibrium point and scaled down by $r^{-(1/2 +
\epsilon)}$, is tight.)

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom