  The standard setting for studying parallel server systems (PSS) at the
diffusion scale is based on the heavy traffic condition (HTC), which assumes
that the underlying static allocation linear program (LP) is critical and has a
unique solution. This solution determines the graph of basic activities, which
identifies the set of activities (i.e., class-server pairs) that are
operational. In this paper we explore the extended HTC, where the LP is merely
assumed to be critical. Because multiple solutions are allowed, multiple sets
of operational activities, referred to as modes, are available. Formally, the
scaling limit for the control problem associated with the model is given by a
so called workload control problem (WCP) in which a cost associated with a
diffusion process is to be minimized by dynamically switching between these
modes. Our main result is that the WCP's value constitutes an asymptotic lower
bound on the cost associated with the PSS model.
