zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Polling and greedy servers on a line. (English) Zbl 0653.90021
A single server moves with speed ν on a line interval (or a circle) of length (circumference) L. Customers, requiring service of constant duration b, arrive on the interval (or circle) at random at mean rate λ customers per unit length per unit time. A customer’s mean wait for service depends partly on the rules governing the server’s motion. We compare two different servers; the polling server and the greedy server. Without knowing the locations of waiting customers, a polling server scans endlessly back and forth across the interval (or clockwise around the circle), stopping only where it encounters a waiting customer. Knowing where customers are waiting, a greedy server always travels toward the current nearest one. Except for certain extreme values of ν, L, b, and λ, the polling and greedy servers are roughly equally effective. Indeed, the simpler polling server is often the better. Theoretical results show, in most cases, that the polling server has a high probability of moving toward the nearest customer, i.e. moving as a greedy server would. The greedy server is difficult to analyze, but was simulated on a computer.
MSC:
90B22Queues and service (optimization)
References:
[1]E.G. Coffman, Jr. and E.N. Gilbert, A continuous polling system, IEEE Trans. Inf. Th., IT-3 2(1986)5 84.
[2]E.G. Coffman, Jr. and M. Hofri, On the expected performance of scanning disks, SIAM J. Comput. 11(1982)60. · Zbl 0478.68036 · doi:10.1137/0211005
[3]E.G. Coffman, Jr. and M. Hofri, Queueing analyses of secondary storage devices, Queueing Systems 1(1986)129. · Zbl 0648.68051 · doi:10.1007/BF01536186
[4]R. Geist and S. Daniel, A continuum of disk scheduling algorithms, Tech. Rep., Computer Science Dept., Clemson University, Clemson, NC (1985); see also S. Daniel and R. Geist, V-SCAN: An adaptive disk scheduling algorithm,Proc. IEEE Int. Symp. on Comp. Sys. Org., New Orleans (1983).
[5]M. Hofri, Disk scheduling: FCFS vs. SSTF revisited, Comm. ACM 23(1980)645. · doi:10.1145/359024.359034
[6]L.B.W. Jolley,Summation of Series (Dover Publications, 1961).
[7]D.E. Knuth,The Art of Computer Programming: Sorting and Searching, Vol. III (Addison-Wesley, Reading, MA, 1973) (see pp. 254-255, 259-264).
[8]T. Teorey and T. Pinkerton, A comparative analysis of disk scheduling policies, Comm. ACM 15(1972)177. · Zbl 0232.68017 · doi:10.1145/361268.361278