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The vision of grid computing is to enable an arbitrary set of general-purpose computers to be recruited dynamically and be interconnected through a general-purpose network for the parallel execution of complex programs. The scale and ubiquity of the Internet makes it the natural network of choice for grid computing. However, for some applications, rate- and delay-guaranteed communication services are needed. These needs are driving the exploration of connection-oriented (CO) optical networks as a candidate for grid computing. In this article, we consider the suitability of CO networks equipped with generalized multiprotocol label switching (GMPLS) control-plane protocols for grid computing. We identify two areas in which current GMPLS implementations need enhancements to better support the needs of grid computing. First, we note a need to improve call setup delays by several orders of magnitude. We describe our proof-of-concept prototype implementation of a hardware-accelerated RSVP-TE engine that cuts setup delays from hundreds of milliseconds (typical in current equipment) to the order of microseconds. Second, noting the availability of different types of CO networks, we present a case for enhancements to control "heterogeneous connections," that is, connections that traverse multiple types of CO networks. We describe a distributed signaling procedure for the setup of such connections.