Some Mathematical Considerations of Time-Sharing Scheduling Algorithms

Shemer, J. E.

doi:10.1145/321386.321389

Cited by 27 publications

(10 citation statements)

References 3 publications

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“…In a priority system working under such a regime long and unknown in advance, service demands in all priority classes are dynamically penalized by degrading their priority degree. This model was first suggested by Shemer [5], who has studied the case where no losses due to the generalized F.B.~ discipline are involved, however his results are in disagreement with ours.…”

Section: Introductionmentioning

confidence: 50%

A Dynamic Time-Sharing Priority Queue

Adiri

1971

J. ACM

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This paper deals with a single server station delivering service to m priority classes (m might be finite or infinite). The arrival process of customers from a jth (j = 1, 2,..., m) priority class (jth customers) to a single server station is a homogenous Poisson process with rate X3 • Service requirements of jth customers are exponentially distributed with mean 1/~. The waiting line consists of infinitely many separate queues all of which obey the FIFO rule. Each priority class is assigned to one of the queues. A newly arrived jth customer joins the end of a predetermined queue. In the ith (i = 1, 2,...) queue a customer is eligible for a certain amount of service following which he either departs when his service requirement has been satisfied or joins the end of the (i + 1)th queue for additional service. When a quantum of service is completed, the server attends to the first customer in the lowest index (highest priority) nonempty queue. In such a priority regime, long and unknown in advance service requirements in all priority classes are dynamically penalized by degrading their priority degree. This paper derives mathematical expressions for calculating the expected total flow time of a jth customer whose service requirement is known.

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Section: Introductionmentioning

confidence: 50%

A Dynamic Time-Sharing Priority Queue

Adiri

1971

J. ACM

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“…These equations, though, provide us with a recursive solution; each E(W,,) is a linear combination of the E(W,~) where 1 < 3 -< i and 1 < m < n, or 1 < n < rn < j < i, while E(Wu) is given explicitly by (14). We can thus solve for E(Wu), E(W21), E(W~2), E(W31), E(W~2), "" in this order.…”

Section: Expected Flow Tzmementioning

confidence: 99%

“…After joining the system, a user is serviced in the same way as in the FB system discussed earlier. This system was studied by Shemer [14], Kleinrock [9], Coffman and Kleinrock [6], and Adiri [1]. The CTSS time-sharing system used a variation of such a scheduling discipline (Scherr [12]), with initial queues and prioritms being assigned according to the program's sizes.…”

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confidence: 99%

A Generalized Multi-Entrance Time-Sharing Priority Queue

Babad

1975

J. ACM

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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-

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“…Additionally, Poisson arrivals have been assumed in multiprogramming analysis of Chang and Wong [6] and Gaver [19], the parallel processing analysis by Coffman [ii], the scheduling analysis by Cox and Smith [13], and Fife [17,18], and the time shared system analysis by Chang [7], Fife [16], Greenberger [20], Kleinrock [22,23], Krishnamoorthi and Wood [24], Scherr [29], and Shemer [30].…”

Section: Poisson Process With Interarrival Time Distributionmentioning

confidence: 99%

“…by Gaver [19], and the analysis of time shared systems by Kleinrock [22,23], Krishnamoorthi and Wood [2h], Scherr [29], and Shemer [30].…”

Section: Poisson Process With Interarrival Time Distributionmentioning

confidence: 99%

Network computer modeling

Bowdon

1972

Proceedings of the ACM Annual Conference on - ACM'72

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Network computers are becoming a reality in the seventies. While systems such as the ARPA network, Carnegie Mellon's PLN, the Collins C-System, CDC's Cybernet, and GE's Time Share Net are coming to fruition, even more grandiose systems are being discussed. These networks all offer the designer the potential of combining the advantages of data base sharing, resource sharing, and load leveling with those of message switching. From a postulation of the essential characteristics of a network computer currently under development, we formulate a queueing theory model for a multiserver system with a finite length priority queue. Then, under the assumptions of Poisson input and exponentially distributed processing times, we use this idealized mathematical model to investigate the steady state stochastic behavior of Jobs in the network. We are particularly interested in the efficiency of computer utilization and the average waiting time for Jobs of different priority classes.

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Some Mathematical Considerations of Time-Sharing Scheduling Algorithms

Cited by 27 publications

References 3 publications

A Dynamic Time-Sharing Priority Queue

A Dynamic Time-Sharing Priority Queue

A Generalized Multi-Entrance Time-Sharing Priority Queue

Network computer modeling

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