Errata: A Queueing System with General-Use and Limited-Use ServersAuthor(s): Linda GreenSource: Operations Research, Vol. 34, No. 1 (Jan. - Feb., 1986), p. 184Published by: INFORMSStable URL: http://www.jstor.org/stable/170684 .

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CORRECTION TO "A QUEUEING SYSTEM WITH GENERAL-USE AND LIMITED-USE SERVERS"

LINDA GREEN Columbia University, New York

Page 171, lines 6 and 7 should read "type R busy servers" and "type G busy servers," respectively, in- stead of "customers in service."

Reference

GREEN, L. 1985. A Queueing System with General-Use and Limited-Use Servers. Opns. Res. 33, 168-182.

CORRECTION TO "OPTIMAL CONTROL OF AN MIMIS QUEUEING SYSTEM"

DONALD S. SZARKOWICZ University of New Hampshire, Durham, New Hampshire

THOMAS W. KNOWLES Illinois Institute of Technology, Chicago, Illinois

Professor Gary Gottlieb of New York University is to be credited with the observation that the proof of Theorem 4 is in error. The sum of two discrete quas- iconvex functions is not always a quasiconvex func- tion.

Theorem 4 holds true if the word quasiconvex is replaced by convex throughout the statement and proof. Theorems 5 and 6 are correct as stated. Because a convex function is also quasiconvex, Theorem 6 may be used to simplify the algorithm for determining the optimal control action in the finite-state case by u*(n; x) = x2, z(n; xi) < x2 :< Z(n; xl). In particular,

a sufficient condition for this simplification is c2(u) convex in u and V(O; x) convex in x2 for all xl. For the terminal cost examples cited, the first is also convex and the second is convex if r2(x2) is convex.

We also note that if c2(u) is convex in u, then in Theorem 7, u'(x) = x2 and the sequence of minimal cost functions retains its convex character.

Reference

SZARKOWICZ, D. S., AND T. W. KNOWLES. 1985. Optimal Control of an M/M/S Queueing System. Opens. Res. 33, 644-660.

Subject classification: 171 errata.

Operations Research Vol. 34, No. 1, January-February 1986

0030-364X/86/3401-0184 $01.25 ? 1986 Operations Research Society of America 184

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