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)
On a batch arrival Poisson queue with generalized vacation. (English) Zbl 0916.60079
Summary: A single server Markovian queue with random batch arrival and generalized vacation is considered where the server goes on vacation of random length as soon as the system becomes empty. On return, if he finds customers waiting in the queue, the server starts serving them one by one till the queue size becomes zero again; otherwise he takes another vacation. The steady state behaviour of this queue under fairly general condition has been studied and we obtain the queue size distributions at stationary point of time, departure point of time and vacation initiation point of time. The departure point of time queue size distribution decomposes into three independent random variables one of which is the queue size of the standard M X /M/1 queue. Also we obtain a simple derivation for Laplace-Stieltjes transform of the queue waiting time distribution, analytically explicit expressions for the system state probabilities and provide their appropriate interpretation. Finally we derive some system performance measures.
MSC:
60K25Queueing theory
60G50Sums of independent random variables; random walks