A model of a growing steady state system

1966 ◽  
Vol 10 (3) ◽  
pp. 387-398 ◽  
Author(s):  
J.N.R. Grainger ◽  
L. Bass
Keyword(s):  
2007 ◽  
Vol 68 (16-18) ◽  
pp. 2313-2319 ◽  
Author(s):  
C.J. Baxter ◽  
J.L. Liu ◽  
A.R. Fernie ◽  
L.J. Sweetlove

Author(s):  
Khalid Alnowibet ◽  
Lotfi Tadj

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. The authors assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.


1994 ◽  
Vol 49 (1-2) ◽  
pp. 108-114 ◽  
Author(s):  
G. H. Schmid ◽  
K. P. Bader ◽  
R. Schulder

In the filamentous cyanobacterium Oscillatoria chalybea deactivation of the S-states starting from steady-state conditions in which S0 = S1 = S2 = S3 = 25% reveals that S3 deactivates to a finite level of approx. 10%. This level is reached under normal conditions between 10-15 seconds. This quasi metastable S3 meets all requirements for S3 in that one flash eliminates this redox conditions to give S4 and therewith molecular oxygen. An analysis of the cyanobacterial S-state system in the 5-state Kok model shows that the S-state population in the dark adapted sample contains no contribution from S-1 or a more reduced condition which under normal conditions is the case for Chlorella or higher plant chloroplasts. Hence under standard conditions, the Oscillatoria condition is a pure Kok-4-condition in which S0 is the most reduced state. Under these conditions S2 seems to deactivate to S1 and S3 to S2 and to a smaller extent to S0. In the presence of the ADRY-reagent Ant-2-p (2-(3-chloro-4-trifluoromethyl)- anilino-3,5-dinitrothiophene) introduced by Renger (Biochim. Biophys. Acta 256,428,1972), which is supposed to specifically act on the S3-state (and thereby on S2), not only the deactivation kinetic of S3 (and S2) is accelerated (hence the life time of the S3-state is shortened), but also the level of metastable S3 becomes practically zero. An analysis of the deactivation pattern shows that the agent changes the mode of deactivation of the entire system. Thus, it is seen that after deactivation of a sample in presence of this agent the dark population of S-states contains the more reduced redox condition S-1 It looks as if in this condition S2 deactivates not only to S1 but also to an appreciable extent by two steps to S-1 Another agent ABDAC (alkyl-benzyl-dimethyl-ammoniumchloride) seems to lengthen the lifetime of the S2 and S3 condition in this cyanobacterium by apparently acting on the membrane condition.


1996 ◽  
Vol 28 (04) ◽  
pp. 1177-1200 ◽  
Author(s):  
Tao Yang ◽  
M. L. Chaudhry

In this paper, we present results for the steady-state system length distributions of the discrete-timeGI/G/1 queue. We examine the system at customer arrival epochs (customer departure epochs) and use the residual service time (residual interarrival time) as the supplementary variable. The embedded Markov chain is ofGI/M/1 type if the embedding points are arrival epochs and is ofM/G/1 type if the embedding points are departure epochs. Using the matrix analytic method, we identify the necessary and sufficient condition for both Markov chains to be positive recurrent. For theGI/M/1 type chain, we derive a matrix-geometric solution for its steady-state distribution and for theM/G/1 type chain, we develop a simple linear transformation that relates it to theGI/M/1 type chain and leads to a simple analytic solution for its steady-state distribution. We also show that the steady-state system length distribution at an arbitrary point in time can be obtained by a simple linear transformation of the matrix-geometric solution for theGI/M/1 type chain. A number of applications of the model to communication systems and numerical examples are also discussed.


2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Renbin Liu ◽  
Zhaohui Deng

This paper examines a discrete-time modified D-policy Geo/G/1 queue with Bernoulli feedback. Using a decomposition method, the steady-state system size distribution at epochn+is obtained. Moreover, the steady-state system size distributions at epochsn-andnare also derived. Two special cases are given. Finally, a wireless local area network is numerically presented to validate the applicability of steady-state system size distribution and its important application in system capacity design.


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