A Generalized Multi-Entrance Time-Sharing Priority Queue

Abstract

A generalized multi-entrance and multipriority M/G/1 time-sharing system is dealt with. The system maintains many separate queues, each identified by two integers, the prmnty level and the entry level The arrival process of users is a homogenous Polsson process, while service requirements are identically distributed and have a finite second moment Upon arrival a user joins one of the levels, through the entry queue of this level In the (n, k)-th queue, where n is the priority level and k is the entry level, a user m eligible to a (finite or lnfimte) quantum of service. If the service requirements of the user are satmfied during the quantum, the user departs, and otherwise he is transferred to the end of the (n ~ 1, k)-th queue for addltmnal service When a quantum of service is completed, the highest priority nonempty level is chosen to be served next, within thin level the queues are scanned according to the prmmty of their entry level, and the user at the head of the highest prmnty nonempty queue is chosen to be served In such a priority dlsclphne, preferred users always get an improved service though the serwce of all users is degraded m proportion to their service requirements Expected flow times and expected number of waiting users are demved and then specialized to the head-of-the-hne M/G/1 prmrlty dlsciphne (in whmh quanta have infinite length and serwce is uninterrupted) and to the FB, time-sharing system. Finally, the generahzed multientrance and multipriomty time-sharing dlsclphne is (numermally) compared with several other time-sharing systems.KEY WORDS AND PHRASES. time-sharing, multi-entrance prmrity queue CR CATEGORIES' 4 32, 4 35 IntroductwnSeveral models of time-sharing computer systems have been described and analyzed in recent years. In these models jobs with short service requirements receive enhanced service at the expense of degraded service for longer requirements; the various models differ in the degree of enhancement they provide. In the simplest time-sharing system (Figure 1), known as a round-robin system, a newly arriving user joins the end of a single queue. This queue is served by a single service facility according to an FIFO discipline. The maximum interval of service time which is given to any user is of limited length, and is called a quantum; if the user's request is fulfilled during this quantum he leaves the system. Otherwise, he joins the end of the queue, behind any recycled users and newly arriving users since the most recent moment at which he entered the queue. Such a system was studied by Kleinrock [8], Adiri and Avi-Itzhak [3], Adiri [2]', and others (see McKinney [11] for additional references).The scheduling discipline of a round-robin system ignores the amount of service, measured in number of service quanta, already given to users already present in the sys-