Matches in SemOpenAlex for { <https://semopenalex.org/work/W3040326075> ?p ?o ?g. }
Showing items 1 to 95 of
95
with 100 items per page.
- W3040326075 abstract "Let X be the constrained random walk on $${mathbb {Z}}_+^2$$ having increments (1, 0), $$(-,1,1)$$ , $$(0,-,1)$$ with jump probabilities $$lambda (M_k)$$ , $$mu _1(M_k)$$ , and $$mu _2(M_k)$$ where M is an irreducible aperiodic finite state Markov chain. The process X represents the lengths of two tandem queues with arrival rate $$lambda (M_k)$$ , and service rates $$mu _1(M_k)$$ , and $$mu _2(M_k)$$ ; the process M represents the random environment within which the system operates. We assume that the average arrival rate with respect to the stationary measure of M is less than the average service rates, i.e., X is assumed stable. Let $$tau _n$$ be the first time when the sum of the components of X equals n for the first time. Let Y be the random walk on $${{mathbb {Z}}} times {{mathbb {Z}}}_+$$ having increments $$(-,1,0)$$ , (1, 1), $$(0,-,1)$$ with probabilities $$lambda (M_k)$$ , $$mu _1(M_k)$$ , and $$mu _2(M_k)$$ . Supposing that the queues share a joint buffer of size n, $$p_n =P_{(x_n,m)}(tau _n < tau _0)$$ is the probability that this buffer overflows during a busy cycle of the system. To the best of our knowledge, the only methods currently available for the approximation of $$p_n$$ are classical large deviations analysis giving the exponential decay rate of $$p_n$$ and rare event simulation. Let $$tau $$ be the first time the components of Y are equal. For $$x in {{mathbb {R}}}_+^2$$ , $$x(1) + x(2) < 1$$ , $$x(1) > 0$$ , and $$x_n = lfloor nx rfloor $$ , we show that $$P_{(n-x_n(1),x_n(2),m)}( tau < infty )$$ approximates $$P_{(x_n,m)}(tau _n < tau _0)$$ with exponentially vanishing relative error as $$nrightarrow infty $$ . For the analysis we define a characteristic matrix in terms of the jump probabilities of (X, M). The 0-level set of the characteristic polynomial of this matrix defines the characteristic surface; conjugate points on this surface and the associated eigenvectors of the characteristic matrix are used to define (sub/super) harmonic functions which play a fundamental role both in our analysis and the computation/approximation of $$P_{(y,m)}(tau < infty )$$ ." @default.
- W3040326075 created "2020-07-10" @default.
- W3040326075 creator A5048862732 @default.
- W3040326075 creator A5057591404 @default.
- W3040326075 date "2020-06-30" @default.
- W3040326075 modified "2023-09-25" @default.
- W3040326075 title "Approximation of the exit probability of a stable Markov modulated constrained random walk" @default.
- W3040326075 cites W1608373512 @default.
- W3040326075 cites W1967783744 @default.
- W3040326075 cites W1975974871 @default.
- W3040326075 cites W2005317775 @default.
- W3040326075 cites W2010764906 @default.
- W3040326075 cites W2017036530 @default.
- W3040326075 cites W2025232464 @default.
- W3040326075 cites W2027096901 @default.
- W3040326075 cites W2031575583 @default.
- W3040326075 cites W2040442483 @default.
- W3040326075 cites W2042616365 @default.
- W3040326075 cites W2044799837 @default.
- W3040326075 cites W2058494911 @default.
- W3040326075 cites W2059124663 @default.
- W3040326075 cites W2059360133 @default.
- W3040326075 cites W2071983356 @default.
- W3040326075 cites W2086035641 @default.
- W3040326075 cites W2090951154 @default.
- W3040326075 cites W2093891645 @default.
- W3040326075 cites W2094909089 @default.
- W3040326075 cites W2101084837 @default.
- W3040326075 cites W2127126889 @default.
- W3040326075 cites W2145189549 @default.
- W3040326075 cites W2155440248 @default.
- W3040326075 cites W2162407085 @default.
- W3040326075 cites W2171723207 @default.
- W3040326075 cites W2626153797 @default.
- W3040326075 cites W2964112947 @default.
- W3040326075 cites W2964315254 @default.
- W3040326075 cites W3100817765 @default.
- W3040326075 cites W4205871929 @default.
- W3040326075 cites W4232753567 @default.
- W3040326075 cites W4233548378 @default.
- W3040326075 cites W4295016751 @default.
- W3040326075 cites W52674758 @default.
- W3040326075 doi "https://doi.org/10.1007/s10479-020-03693-7" @default.
- W3040326075 hasPublicationYear "2020" @default.
- W3040326075 type Work @default.
- W3040326075 sameAs 3040326075 @default.
- W3040326075 citedByCount "1" @default.
- W3040326075 countsByYear W30403260752021 @default.
- W3040326075 crossrefType "journal-article" @default.
- W3040326075 hasAuthorship W3040326075A5048862732 @default.
- W3040326075 hasAuthorship W3040326075A5057591404 @default.
- W3040326075 hasBestOaLocation W30403260752 @default.
- W3040326075 hasConcept C104247578 @default.
- W3040326075 hasConcept C105795698 @default.
- W3040326075 hasConcept C114614502 @default.
- W3040326075 hasConcept C118615104 @default.
- W3040326075 hasConcept C121194460 @default.
- W3040326075 hasConcept C121332964 @default.
- W3040326075 hasConcept C160403385 @default.
- W3040326075 hasConcept C199360897 @default.
- W3040326075 hasConcept C2778113609 @default.
- W3040326075 hasConcept C33923547 @default.
- W3040326075 hasConcept C41008148 @default.
- W3040326075 hasConcept C62520636 @default.
- W3040326075 hasConceptScore W3040326075C104247578 @default.
- W3040326075 hasConceptScore W3040326075C105795698 @default.
- W3040326075 hasConceptScore W3040326075C114614502 @default.
- W3040326075 hasConceptScore W3040326075C118615104 @default.
- W3040326075 hasConceptScore W3040326075C121194460 @default.
- W3040326075 hasConceptScore W3040326075C121332964 @default.
- W3040326075 hasConceptScore W3040326075C160403385 @default.
- W3040326075 hasConceptScore W3040326075C199360897 @default.
- W3040326075 hasConceptScore W3040326075C2778113609 @default.
- W3040326075 hasConceptScore W3040326075C33923547 @default.
- W3040326075 hasConceptScore W3040326075C41008148 @default.
- W3040326075 hasConceptScore W3040326075C62520636 @default.
- W3040326075 hasLocation W30403260751 @default.
- W3040326075 hasLocation W30403260752 @default.
- W3040326075 hasLocation W30403260753 @default.
- W3040326075 hasOpenAccess W3040326075 @default.
- W3040326075 hasPrimaryLocation W30403260751 @default.
- W3040326075 hasRelatedWork W2025348871 @default.
- W3040326075 hasRelatedWork W2058591591 @default.
- W3040326075 hasRelatedWork W2106827195 @default.
- W3040326075 hasRelatedWork W2149071482 @default.
- W3040326075 hasRelatedWork W2597526809 @default.
- W3040326075 hasRelatedWork W2952539738 @default.
- W3040326075 hasRelatedWork W4292734940 @default.
- W3040326075 hasRelatedWork W107107499 @default.
- W3040326075 hasRelatedWork W121402011 @default.
- W3040326075 hasRelatedWork W2467037348 @default.
- W3040326075 isParatext "false" @default.
- W3040326075 isRetracted "false" @default.
- W3040326075 magId "3040326075" @default.
- W3040326075 workType "article" @default.