Matching moments to phase distributions: Mixtures of erlang distributions of common order

1989 ◽  
Vol 5 (4) ◽  
pp. 711-743 ◽  
Author(s):  
Mary A. Johnson ◽  
Michael R. Taaffe
Keyword(s):  
Erlang Distributions ◽  
Matching Moments

scholarly journals Stable scheduling of single machine with probabilistic parameters

2017 ◽  
Vol 65 (2) ◽  
pp. 219-231 ◽  
Author(s):  
W. Bożejko ◽  
P. Rajba ◽  
M. Wodecki
Keyword(s):  
Tabu Search ◽  
Single Machine ◽  
Random Variables ◽  
Global Optimum ◽  
Total Weighted Tardiness ◽  
Independent Random Variables ◽  
Stochastic Version ◽  
Weighted Tardiness ◽  
Deterministic Problem ◽  
Erlang Distributions

Abstract We consider a stochastic variant of the single machine total weighted tardiness problem jobs parameters are independent random variables with normal or Erlang distributions. Since even deterministic problem is NP-hard, it is difficult to find global optimum for large instances in the reasonable run time. Therefore, we propose tabu search metaheuristics in this work. Computational experiments show that solutions obtained by the stochastic version of metaheuristics are more stable (i.e. resistant to data disturbance) than solutions generated by classic, deterministic version of the algorithm.

Chi-square Mixture of Erlang Distributions

2006 ◽  
Vol 1 (5) ◽  
pp. 487-495
Author(s):  
M.R. Zaman . ◽  
M.K. Roy . ◽  
N. Akhter .
Keyword(s):  
Chi Square ◽  
Erlang Distributions

The general bulk queue as a matrix factorisation problem of the Wiener-Hopf type. Part II.

1975 ◽  
Vol 7 (3) ◽  
pp. 647-655 ◽  
Author(s):  
John Dagsvik
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Time Process ◽  
Waiting Time Process ◽  
Bulk Queue ◽  
Erlang Distributions ◽  
Matrix Factorisation

In a previous paper (Dagsvik (1975)) the waiting time process of the single server bulk queue is considered and a corresponding waiting time equation is established. In this paper the waiting time equation is solved when the inter-arrival or service time distribution is a linear combination of Erlang distributions. The analysis is essentially based on algebraic arguments.

A geometric interpretation of the relations between the exponential and generalized Erlang distributions

1982 ◽  
Vol 14 (04) ◽  
pp. 885-897 ◽  
Author(s):  
Michel Dehon ◽  
Guy Latouche
Keyword(s):  
Vector Space ◽  
Convex Subset ◽  
Geometric Interpretation ◽  
Distribution Functions ◽  
Real Vector ◽  
Exponential Distributions ◽  
Geometric Aspect ◽  
Linear Combinations ◽  
Exponential Random Variables ◽  
Erlang Distributions

Linear combinations of exponential distribution functions are considered, and the class of distribution functions so obtainable is investigated. Convex combinations correspond to hyperexponential distributions, while non-convex combinations yield, among other, generalized Erlang distributions obtainable as sums of independent exponential random variables with different parameters. For a given number n of different exponential distributions, the class investigated is an (n – 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions. The geometric aspect of this subset is revealed, together with the location of hyperexponential and generalized Erlang distributions.

A fitting method with generalized Erlang distributions

2011 ◽  
Vol 19 (7) ◽  
pp. 1507-1517 ◽  
Author(s):  
Kyungsup Kim ◽  
Nigel Thomas
Keyword(s):  
Fitting Method ◽  
Erlang Distributions

Exact average run lengths of cusum schemes for erlang distributions

1998 ◽  
Vol 17 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Seven Knoth ◽  
Seven Knoth
Keyword(s):  
Run Lengths ◽  
Erlang Distributions

scholarly journals Probabilistic Inventory Model Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment

2018 ◽  
Vol 15 ◽  
pp. 8051-8069
Author(s):  
H. A. Ferganya ◽  
Osama Mahmoud Hollah
Keyword(s):  
Random Variable ◽  
Inventory Model ◽  
Inventory Level ◽  
Periodic Review ◽  
Fuzzy Environment ◽  
Holding Cost ◽  
Annual Total ◽  
Probabilistic Inventory Model ◽  
Erlang Distributions ◽  
Periodic Review Inventory

This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions). The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.

Sign in / Sign up

Export Citation Format

Share Document