A generalization of a waiting time problem

1990 ◽  
Vol 22 (3) ◽  
pp. 758-760 ◽  
Author(s):  
B. S. El-Desouky ◽  
S. A. Hussen
Keyword(s):  
Waiting Time ◽  
Special Cases ◽  
Time Problem ◽  
Waiting Time Problem ◽  
Finite Memory

An urn contains m types of balls of unequal numbers. Let ni be the number of balls of type i, i = 1, 2, …, m. Balls are drawn with replacement until first duplication. In the case of finite memory of order k, the distribution of Ym,k, the number of drawings required, is discussed. Special cases are obtained.

scholarly journals On a generalization of a waiting time problem and some combinatorial identities

2015 ◽  
Vol 52 (04) ◽  
pp. 981-989
Author(s):  
B. S. El-desouky ◽  
F. A. Shiha ◽  
A. M. Magar
Keyword(s):  
Waiting Time ◽  
Probability Function ◽  
Stirling Numbers ◽  
Combinatorial Identities ◽  
Special Cases ◽  
Time Problem ◽  
Probability Of Success ◽  
Waiting Time Problem ◽  
Finite Memory ◽  
Generalized Harmonic Numbers

In this paper we give an extension of the results of the generalized waiting time problem given by El-Desouky and Hussen (1990). An urn contains m types of balls of unequal numbers, and balls are drawn with replacement until first duplication. In the case of finite memory of order k, let ni be the number of type i, i = 1, 2, …, m. The probability of success pi = ni/N, i = 1, 2, …, m, where ni is a positive integer and Let Ym,k be the number of drawings required until first duplication. We obtain some new expressions of the probability function, in terms of Stirling numbers, symmetric polynomials, and generalized harmonic numbers. Moreover, some special cases are investigated. Finally, some important new combinatorial identities are obtained.

scholarly journals A generalization of a waiting time problem

1990 ◽  
Vol 22 (03) ◽  
pp. 758-760 ◽  
Author(s):  
B. S. El-Desouky ◽  
S. A. Hussen
Keyword(s):  
Waiting Time ◽  
Special Cases ◽  
Time Problem ◽  
Waiting Time Problem ◽  
Finite Memory

An urn contains m types of balls of unequal numbers. Let ni be the number of balls of type i, i = 1, 2, …, m. Balls are drawn with replacement until first duplication. In the case of finite memory of order k, the distribution of Ym,k, the number of drawings required, is discussed. Special cases are obtained.

scholarly journals On a generalization of a waiting time problem and some combinatorial identities

2015 ◽  
Vol 52 (4) ◽  
pp. 981-989
Author(s):  
B. S. El-desouky ◽  
F. A. Shiha ◽  
A. M. Magar
Keyword(s):  
Waiting Time ◽  
Probability Function ◽  
Stirling Numbers ◽  
Combinatorial Identities ◽  
Special Cases ◽  
Time Problem ◽  
Probability Of Success ◽  
Waiting Time Problem ◽  
Finite Memory ◽  
Generalized Harmonic Numbers

In this paper we give an extension of the results of the generalized waiting time problem given by El-Desouky and Hussen (1990). An urn contains m types of balls of unequal numbers, and balls are drawn with replacement until first duplication. In the case of finite memory of order k, let ni be the number of type i, i = 1, 2, …, m. The probability of success pi = ni/N, i = 1, 2, …, m, where ni is a positive integer and Let Ym,k be the number of drawings required until first duplication. We obtain some new expressions of the probability function, in terms of Stirling numbers, symmetric polynomials, and generalized harmonic numbers. Moreover, some special cases are investigated. Finally, some important new combinatorial identities are obtained.

On the single server queue with preemptive service interruptions

1971 ◽  
Vol 8 (4) ◽  
pp. 835-837 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
Stochastic System ◽  
Single Server ◽  
Single Server Queue ◽  
Service Interruptions ◽  
Time Problem ◽  
Server Queue ◽  
Waiting Time Problem ◽  
Limiting Behaviour

In [4], the limiting behaviour of a stochastic system with two types of input was investigated by reducing the problem to the solution of an integral equation. In this note we use the same approach to study the equilibrium waiting time problem for the general single server queue with preemptive service interruptions. (For a comprehensive account of the existing literature on queues with service interruptions we refer to [2] and [3].)

On a waiting time problem in physiology

1964 ◽  
Vol 51 (21) ◽  
pp. 512-513
Author(s):  
M. ten Hoopen
Keyword(s):  
Waiting Time ◽  
Time Problem ◽  
Waiting Time Problem

scholarly journals A waiting time problem arising from the study of multi-stage carcinogenesis

2009 ◽  
Vol 19 (2) ◽  
pp. 676-718 ◽  
Author(s):  
Rick Durrett ◽  
Deena Schmidt ◽  
Jason Schweinsberg
Keyword(s):  
Waiting Time ◽  
Multi Stage ◽  
Time Problem ◽  
Waiting Time Problem

On the single server queue with preemptive service interruptions

1971 ◽  
Vol 8 (04) ◽  
pp. 835-837 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
Stochastic System ◽  
Single Server ◽  
Single Server Queue ◽  
Service Interruptions ◽  
Time Problem ◽  
Server Queue ◽  
Waiting Time Problem ◽  
Limiting Behaviour

In [4], the limiting behaviour of a stochastic system with two types of input was investigated by reducing the problem to the solution of an integral equation. In this note we use the same approach to study the equilibrium waiting time problem for the general single server queue with preemptive service interruptions. (For a comprehensive account of the existing literature on queues with service interruptions we refer to [2] and [3].)

scholarly journals Waiting time distributions of competing patterns in higher-order Markovian sequences

2005 ◽  
Vol 42 (4) ◽  
pp. 977-988 ◽  
Author(s):  
John A. D. Aston ◽  
Donald E. K. Martin
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Finite Markov Chain ◽  
Waiting Time Distribution ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding ◽  
Start Up ◽  
Time Problem ◽  
Waiting Time Problem ◽  
General Order

Competing patterns are compound patterns that compete to be the first to occur pattern-specific numbers of times. They represent a generalisation of the sooner waiting time problem and of start-up demonstration tests with both acceptance and rejection criteria. Through the use of finite Markov chain imbedding, the waiting time distribution of competing patterns in multistate trials that are Markovian of a general order is derived. Also obtained are probabilities that each particular competing pattern will be the first to occur its respective prescribed number of times, both in finite time and in the limit.

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