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^ i PJi ki sjxi bki ;

Since everything must be either a process or a channel, forks must be processes A Fork continuously loops waiting for a message from one of its users (either its left-hand or right-hand philosopher) When it gets a message from one indicating a fork pick-up, it waits for another indicating a fork put-down (While it might be more tasteful to indicate pick-ups versus put-downs via different kinds of messages or message contents, this protocol using null messages suffices) In JCSP, this can be written as:

17:25

DLogicalDevice:: DLogicalDevice() { if (iCodeSeg) { __DEBUG_EVENT(EEventUnloadLdd, iCodeSeg); iCodeSeg->ScheduleKernelCleanup(EFalse); } }

^ where the single-source transform Pj i i sjxi is given in Theorem 17.4.1. ik Unlike for the aggregate mean, for the aggregate variance we evidently need to perform n separate inversions to calculate viji tjxi for each i and then add to calculate V tjj; x in Eq. (17.24). (We assume that the within-level variances wiji tjxi , if included, are speci ed directly.) Hence, we suggest calculating only the conditional mean in real time to perform control, and occasionally calculating the conditional variance to evaluate the accuracy of the conditional mean.

The function call ScheduleKernelCleanup(EFalse) unloads the associated DLL with module reason KModuleEntryReasonProcessDetach, ensuring that the any static data initialized at DLL load time is destroyed. The EFalse parameter indicates that the code segment is not to be immediately destroyed (since we are still using the code to run the destructor), but is to be added to the garbage list and scheduled for deletion when the null thread next runs.

^ The most complicated part of the conditional aggregate mean transform M sjj; x in ^ Eq. (17.25) is the matrix inverse I q s 1 in the transform of the single-source transition probability in Eq. (17.14). Since the matrix inverse calculation can be a computational burden when the number of levels is large, it is natural to seek approximations that avoid this matrix inverse. We describe such approximations in this section. The matrix inverse I q s 1 is a compact representation for the series PI n n 0 q s . For P tjx , it captures the possibility of any number of transitions up to time t. However, if the holding times in the levels are relatively long in the time scales relevant for control, then the mean for times t of interest will only be signi cantly affected by a very few transitions. Indeed, often only a single transition need be considered. The single-transition approximation is obtained by making the Markov chain absorbing after one transition. Hence, the single-transition approximation is simply Pjk tjx % Hjk tjx ; j T k; and Pjj tjx % Gjc tjx Hjj tjx 17:26

class Fork implements CSProcess { private final AltingChannelInput[] fromPhil; Fork(AltingChannelInput l, AltingChannelInput r) { fromPhil = new AltingChannelInput[] { l, r }; } public void run() { Alternative alt = new Alternative(fromPhil); for (;;) { int i = altselect(); fromPhil[i]read(); fromPhil[i]read(); } } }

for Hjk tjx in Eq. (17.9) and Gj tjx in Eq. (17.9). From Eq. (17.26) we see that no inversion is needed. Alternatively, we can develop a two-transition approximation. (Extensions to higher numbers are straightforward.) Modifying the proof of Theorem 17.4.1 in a straightforward manner, we obtain Pjk tjx % for j T k and Pjj tjx % Gjc tjx P

In the previous section, I discussed how device drivers are loaded, creating LDD and PDD factory objects. The next step in using a device driver is to open a channel through which requests can be made. User-side code does this by making a call to RBusLogicalChannel::DoCreate(). (In reality, a client cannot call this method directly, since it is protected. It is called indirectly, via a driver-speci c wrapper function, usually named Open(), although this doesn t affect our current discussion.)

17:27

The Butler process makes sure that at most N-1 (ie, four here) philosophers are seated at any given time It does this by enabling both enter and exit messages if there are enough seats, but only exit messages otherwise Because Alternative operates on arrays of alternatives, this requires a bit of manipulation to set up (Some other utilities in JCSP could be used to simplify this)

inline TInt DoCreate(const TDesC& aDevice, const TVersion& aVer, TInt aUnit, const TDesC* aDriver, const TDesC8* anInfo, TOwnerType aType=EOwnerProcess, TBool aProtected=EFalse);

Plj Flj t u dHjl ujx :

17:28

The exit channels are placed before the enter channels in the chans array so that the proper channel will be read no matter which Alternative is used The fairSelect is employed here to ensure that the same four philosophers are not always chosen if a fifth is also trying to enter