Multilevel Queues with Extremal Priorities

ABSTRACT

This paper deals with a single server serving N priority classes (N being finite or infinite) and working under an FBz regime, namely, one in which the waiting line consists of infinitely many separate queues obeying the FIFO rule. Each priority class is assigned to one of the queues. A customer from the kth priority class (“k-customer”) in the nth queue is eligible for &thgr;n,k time units of service, at the end of which he either departs, because his requirement is satisfied, or joins the tail of the (n + 1)-th queue. When a quantum of service is completed, the server turns to the first customer in the lowest index (highest priority) nonempty queue. The arrival process of k-customers is assumed to be homogeneous Poisson, and their service requirements are independent, generally distributed, random variable. A set of recursive linear equations is derived for the expected flow time of a k-customer whose service requirement is known, and some examples are discussed and presented graphically. This paper corrects some errors in an earlier paper by the second author.

REFERENCES

• 1: Igal Adiri, A Dynamic Time-Sharing Priority Queue, Journal of the ACM (JACM), v.18 n.4, p.603-610, Oct. 1971 [doi>10.1145/321662.321675]
• 2: ADlm, I , AND AVa-ITznAZ, B A time-sharing model with many queues Oper Res 17, 6 (1969), 1077- 1089
• 3: Edward G. Coffman , Leonard Kleinrock, Feedback Queueing Models for Time-Shared Systems, Journal of the ACM (JACM), v.15 n.4, p.549-576, Oct. 1968 [doi>10.1145/321479.321483]
• 4: CoNwAY, R.W., MAXWELL, W.L., AND MILLER, L.W Theory of Scheduhng Addison-Wesley, Reading, Mass., 1967
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Queueing theory

Additional Classification:
  D. Software
  D.4 OPERATING SYSTEMS
      D.4.8 Performance
          Subjects: Queueing theory

General Terms:
Performance, Theory