**6.2.3 Idling periodic server**

An idling periodic server is a special kind of a deferrable server containing an idle task (with lowest priority). The idle task is switched in if no higher priority task is ready, effectively idling away the remaining capacity. In order to save memory needed for storing the task control block and the stack of the idle task, one idle task is shared between all idling periodic servers in the system.

## **6.3 Virtual timers**

When the server budget is depleted an event must be triggered, to guarantee that a server does not exceed its budget. We present a general approach for handling budget depletion and introduce the notion of *virtual timers*, which are events relative to server's budget consumption.

We can implement virtual timers by adding a *virtual server queue* for *each* server, denoted by *σi*.*vq*. Similarly to the server queues introduced earlier, when a server is switched in, its virtual server queue is activated. The difference is that the virtual server queue is not synchronized with the stopwatch queue, since during the inactive period a server does not consume any of its budget. When a server is switched out, its virtual server queue is deactivated.

The relative time representation by RELTEQ allows for a more efficient virtual queue activation than an absolute time representation does. An absolute time representation (e.g. in (Behnam et al., 2008; Inam et al., 2011)) requires to recompute the expiration time for *all* the events in a virtual server queue upon switching in the corresponding server, which is linear in the number of events. In our RELTEQ-based virtual queues the events are stored relative to each other and their expiration times do not need to be recomputed upon queue activation. Note that it will never be necessary to handle an expired virtual event upon queue activation, since such an event would have been already handled before the corresponding server was switched out. Therefore, our HSF design exhibits a constant time activation of a virtual server queue.
