  In areas such as computer software and hardware, manufacturing systems, and
transportation, engineers encounter networks with arbitrarily large numbers of
isomorphic subprocesses. Parameterized systems provide a framework for modeling
such networks. The analysis of parameterized systems is a challenge as some key
properties such as nonblocking and deadlock-freedom are undecidable even for
the case of a parameterized system with ring topology. In this paper, we
introduce \textit{Parameterized-Chain Networks} (PCN) for modeling of networks
containing several linear parameterized segments. Since deadlock analysis is
undecidable, to achieve a tractable subproblem we limit the behavior of
subprocesses of the network using our previously developed mathematical notion
`weak invariant simulation.' We develop a dependency graph for analysis of PCN
and show that partial and total deadlocks of the proposed PCN are characterized
by full, consistent subgraphs of the dependency graph. We investigate deadlock
in a traffic network as an illustrative example. This document contains all the
details and proofs of the study.
