  We study the problem of metrical service systems with multiple servers
(MSSMS), which generalizes two well-known problems -- the $k$-server problem,
and metrical service systems. The MSSMS problem is to service requests, each of
which is an $l$-point subset of a metric space, using $k$ servers, with the
objective of minimizing the total distance traveled by the servers.
  Feuerstein initiated a study of this problem by proving upper and lower
bounds on the deterministic competitive ratio for uniform metric spaces. We
improve Feuerstein's analysis of the upper bound and prove that his algorithm
achieves a competitive ratio of $k({{k+l}\choose{l}}-1)$. In the randomized
online setting, for uniform metric spaces, we give an algorithm which achieves
a competitive ratio $\mathcal{O}(k^3\log l)$, beating the deterministic lower
bound of ${{k+l}\choose{l}}-1$. We prove that any randomized algorithm for
MSSMS on uniform metric spaces must be $\Omega(\log kl)$-competitive. We then
prove an improved lower bound of ${{k+2l-1}\choose{k}}-{{k+l-1}\choose{k}}$ on
the competitive ratio of any deterministic algorithm for $(k,l)$-MSSMS, on
general metric spaces. In the offline setting, we give a pseudo-approximation
algorithm for $(k,l)$-MSSMS on general metric spaces, which achieves an
approximation ratio of $l$ using $kl$ servers. We also prove a matching
hardness result, that a pseudo-approximation with less than $kl$ servers is
unlikely, even for uniform metric spaces. For general metric spaces, we
highlight the limitations of a few popular techniques, that have been used in
algorithm design for the $k$-server problem and metrical service systems.
