Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Block-Structured Supermarket Models   Supermarket models are a class of parallel queueing networks with an adaptive
control scheme that play a key role in the study of resource management of,
such as, computer networks, manufacturing systems and transportation networks.
When the arrival processes are non-Poisson and the service times are
non-exponential, analysis of such a supermarket model is always limited,
interesting, and challenging.
  This paper describes a supermarket model with non-Poisson inputs: Markovian
Arrival Processes (MAPs) and with non-exponential service times: Phase-type
(PH) distributions, and provides a generalized matrix-analytic method which is
first combined with the operator semigroup and the mean-field limit. When
discussing such a more general supermarket model, this paper makes some new
results and advances as follows: (1) Providing a detailed probability analysis
for setting up an infinite-dimensional system of differential vector equations
satisfied by the expected fraction vector, where "the invariance of environment
factors" is given as an important result. (2) Introducing the phase-type
structure to the operator semigroup and to the mean-field limit, and a
Lipschitz condition can be obtained by means of a unified matrix-differential
algorithm. (3) The matrix-analytic method is used to compute the fixed point
which leads to performance computation of this system. Finally, we use some
numerical examples to illustrate how the performance measures of this
supermarket model depend on the non-Poisson inputs and on the non-exponential
service times. Thus the results of this paper give new highlight on
understanding influence of non-Poisson inputs and of non-exponential service
times on performance measures of more general supermarket models.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg