  The paper considers multivariate discrete random sums with equal number of
summands. Such distributions describe the total claim amount received by a
company in a fixed time point. In Queuing theory they characterize cumulative
waiting times of customers up to time t. In Theory of branching processes they
model the number of heirs at a fixed point in time.
  Here some general properties and formulae for numerical characteristics of
these distributions are derived and some particular cases are considered.
