1. A system for facilitating assignments of tasks to resources in particular time intervals based on usage patterns and resource capacities, the system comprising: one or more interfaces that: receive a first set of electronic communications from one or more monitoring devices; receive a second set of electronic communications from one or more resource-controlling devices; transmit a third set of electronic communications to one or more resource-controlling devices; receive a fourth set of electronic communications from one or more client devices; and transmit a fifth set of electronic communications to one or more client devices; a usage monitor that: monitors the first set of electronic communications, received via the one or more interfaces, from the one or more monitoring devices to identify resource-usage durations; and updates a usage-patterns data store to associate each of one or more entities and each of one or more task types with usage data based on one or more of the identified resource-usage durations; a timetable mirror that: monitors the second set of electronic communications, received via the one or more interfaces, from the one or more resource-controlling devices to identify updates to timetables of the resources that indicate capacities to accept new tasks during particular time periods; and updates a mirrored timetable data store based on the identified updates to the timetables; one or more load-balancing processors that: detect a first electronic communication of the fourth set of electronic communications, received via the one or more interfaces from a client device of the one or more client devices, that corresponds to an electronic request to use a resource to complete a task, wherein the resource comprises medical equipment and/or laboratory equipment; identify a task type of the task; identify a client that corresponds to the electronic request; access usage data, from the usage-patterns data store, associated with the client and the task type; identify, based on the usage data, a task-performance duration that corresponds to the electronic request for using the resource; define a task-assignment duration based on the task-performance duration and a buffer time period, wherein the buffer time period includes a time period for resource restoration; access, for each of one or more resources and from the mirrored timetable data store, a timetable of the resource that indicates a capacity to accept new tasks during particular time periods; identify an availability in the timetable of a resource of the one or more resources that is of a duration that is at least as long as the task-assignment duration; generate a second electronic communication to be transmitted via the one or more interfaces to the client device that identifies a start time of the availability; detect a third electronic communication received via the one or more interfaces from the client device that accepts the start time; and generate a fourth electronic communication to be transmitted via the one or more interfaces to a device controlling use of the resource that identifies the client, the task and the availability.