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The main problem involves tax and pay accumulators If a single payroll supplier accumulates all of this information for a full calendar year, then it will agree to issue W-2 forms to the company for its employees at the end of the year However, if the supplier is taking over for only part of a year, it will not guarantee the accuracy of the W-2 forms, only issue a W-2 for the period during which it provided services, or not agree to issue the forms at all This means that the company must manually produce all W-2 forms at the end of the year (which can be a considerable chore if there are thousands of employees) or else allow the supplier to issue a W-2 for just that portion of the year during which it provided services to the company and then issue a second W-2 either internally or with the services of yet another supplier The best way to avoid this problem is to only switch payroll suppliers at the end of the calendar year, when payroll and tax accumulators are complete and can be reported as such on employee W-2 forms

In order to provide these properties, many of the techniques from past chapters must be used That includes synchronization primitives (s 5 and 6), lock free programming ( 1 0), and, an awareness of concur rency hazards ( 1 1 ) Not only is this fairly extensive background necessary, but there are multiple approaches from which to choose 1 Coarse-grained locking is the easiest scheme to implement A single lock per container is used, and all read /write operations acquire this single lock This guarantees contention any time more than one thread accesses the same container This is what sequential oriented libraries typically provide because scalability is a distant concern Scalability can be improved by using coarse-grained reader/ writer locks instead of mutually exclusive locks-especially when reads outnumber writes, which is often the case-but often not satisfactorily 2 Fine-grained locking is advantageous when the data structure can be broken into distinct pieces Only threads that access the same piece at the same time will experience contention Such a scheme can take two forms: associating locks with actual parts of the data struc ture, such as individual nodes in a linked list, or by having some kind of mapping from an arbitrary part to a set of collection-wide locks How you'd do the first is probably obvious-although having low overhead locks, such as single word spin locks, becomes more important-but the second approach may be less obvious Striping is the most commonly used technique, enabling you to have fewer locks than pieces To illustrate striping, a structure with P pieces will have L locks, and when a thread needs to access a particular piece of the structure, pn, it just acquires lock number pn % L ("Piece" has different meanings for

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1 Show that if X1 is the waiting time for the rst binomial success and X2 is the waiting time for the second binomial success, then X1 + X2 has a negative binomial distribution with r = 2 2 Show that the expected waiting time for the pattern HT with a fair coin is four tosses