  RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA)
strand which is complementary to a single-stranded DNA template. From the
perspective of physicists, an RNAP is a molecular motor that utilizes chemical
energy input to move along the track formed by a DNA. In many circumstances,
which are described in this paper, a large number of RNAPs move simultaneously
along the same track; we refer to such collective movements of the RNAPs as
RNAP traffic. Here we develop a theoretical model for RNAP traffic by
incorporating the steric interactions between RNAPs as well as the
mechano-chemical cycle of individual RNAPs during the elongation of the mRNA.
By a combination of analytical and numerical techniques, we calculate the rates
of mRNA synthesis and the average density profile of the RNAPs on the DNA
track. We also introduce, and compute, two new measures of fluctuations in the
synthesis of RNA. Analyzing these fluctuations, we show how the level of {\it
intrinsic noise} in mRNA synthesis depends on the concentrations of the RNAPs
as well as on those of some of the reactants and the products of the enzymatic
reactions catalyzed by RNAP. We suggest appropriate experimental systems and
techniques for testing our theoretical predictions.
