ISSN 0032-9460, Problems of Information Transmission, 2015, Vol. 51, No. 3, pp. 299–305.
Pleiades Publishing, Inc., 2015.
Original Russian Text
I.S. Kargin, E.M. Khorov, A.I. Lyakhov, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 3, pp. 105–111.
COMMUNICATION NETWORK THEORY
A Mathematical Method for Packet Loss
Ratio Estimation for a Multipath Route
in the Presence of Correlated Errors
Kharkevich Institute for Information Transmission Problems,
Russian Academy of Sciences, Moscow, Russia
e-mail: email@example.com, firstname.lastname@example.org, email@example.com
Received April 23, 2015; in ﬁnal form, June 9, 2015
Abstract—We consider two-hop multipath routing in wireless networks. Errors occurring in
transmission through diﬀerent paths can be correlated. We explicitly ﬁnd eigenvectors and
eigenvalues of the transition probability matrix describing the system. We obtain an expression
for the delivery probability of a packet to a ﬁnal destination.
In recent years, in wireless networks there is considerable growth of multimedia traﬃc sensitive
to the quality of service (QoS) and especially to the packet loss ratio (PLR). The problem of
estimating and reducing the PLR can be solved at the physical layer, with the use of error-resistant
coding [1–3], and also at the medium access layer and with routing [4–10].
In the present paper, we consider the possibility of reducing the PLR both at the medium
access layer—this can be achieved by making several attempts for packet transmission at route
nodes —and by using multipath routing, i.e., delivering the same packets through several paths
simultaneously [9, 10], which is eﬃcient in naturally broadcasting wireless networks. In existing
protocols based on multipath routing, it is usually assumed in PLR estimation that errors occurring
on diﬀerent packet transmission paths are independent [11–13]. However, in  it was shown that
such errors can be correlated. Therefore, in [15,16] there were proposed methods for estimating the
degree of error correlation occurring on two paths and for distributed computing of this estimation.
Nevertheless, modern wireless networks are high-density, and the number of paths in them can be
greater than two. As far as the authors are concerned, presently there is no eﬃcient approach to
estimating and handling with the error correlation occurring on more than two paths.
In this paper we propose a method to compute the PLR for a multipath route under the as-
sumption of the general form of error correlation occurring on N paths.
2. PROBLEM STATEMENT
We consider two-hop routing in a wireless network consisting of a source, its N one-hop neighbors
(relays), and D destinations; see Fig. 1. The source makes s ≥ 1 attempts to transmit each packet.
When a relay i =
1,N ﬁrst receives a packet, it makes a ﬁxed number r
≥ 1 of attempts to
transmit it. If several relays have received a packet from the source, their transmission attempts
The research was carried out at the Institute for Information Transmission Problems of the Russian
Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.