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  • 1
    Electronic Resource
    Electronic Resource
    Numerical analysis for bulk-arrival queueing systems: Root-finding and steady-state probabilities inGI r /M/1 queues (1987)
    Springer
    Annals of operations research 8 (1987), S. 307-320 
    Details
    ISSN: 1572-9338
    Keywords: Roots ; group arrival ; single server ; probability distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Queueing theorists have presented, as solutions to many queueing models, probability generating functions in which state probabilities are expressed as functions of the roots of characteristic equations, evaluation of the roots in particular cases being left to the reader. Many users have complained that such solutions are inadequate. Some queueing theorists, in particular Neuts [6], rather than use Rouché's theorem to count roots and an equation-solver to find them, have developed new algorithms to solve queueing problems numerically, without explicit calculation of roots. Powell [7] has shown that in many bulk service queues arising in transportation models, characteristic equations can be solved and state probabilities can be found without serious difficulty, even when the number of roots to be found is large. We have slightly modified Powell's method, and have extended his work to cover a number of bulk-service queues discussed by Chaudhry et al. [1] and a number of bulk-arrival queues discussed in the present paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187099
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Exact and approximate numerical solutions of steady-state distributions arising in the queueGI/G/1 (1992)
    Springer
    Queueing systems 10 (1992), S. 105-152 
    Details
    ISSN: 1572-9443
    Keywords: Roots ; queueing time ; idle time ; interdeparture time ; approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we first obtain, in a unified way, closed-form analytic expressions in terms of roots of the so-called characteristic equation (c.e.), and then discuss the exact numerical solutions of steady-state distributions of (i) actual queueing time, (ii) virtual queueing time, (iii) actual idle time, and (iv) interdeparture time for the queueGI/R/1, whereR denotes the class of distributions whose Laplace-Stieltjes transforms (LSTs) are rational functions (ratios of a polynomial of degree at mostn to a polynomial of degreen). For the purpose of numerical discussions of idle- and interdeparture-time distributions, the interarrival-time distribution is also taken to belong to the classR. It is also shown that numerical computations of the idle-time distribution ofR/G/1 queues can be done even ifG is not taken asR. Throughout the discussions it is assumed that the queue discipline is first-come-first-served (FCFS). For the tail of the actual queueing-time distribution ofGI/R/1, approximations in terms of one or more roots of the c.e. are also discussed. If more than one root is used, they are taken in ascending order of magnitude. Numerical aspects have been tested for a variety of complex interarrival- and service-time distributions. The analysis is not restricted to generalized distributions with phases such as Coxian-n (C n ), but also covers nonphase type distributions such as uniform (U) and deterministic (D). Some numerical results are also presented in the form of tables and figures. It is expected that the results obtained from the present study should prove to be useful not only to practitioners, but also to queueing theorists who would like to test the accuracies of inequalities, bounds or approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158522
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  • 3
    Electronic Resource
    Electronic Resource
    Computational analysis of steady-state probabilities of M/Ga,b/1 and related nonbulk queues (1987)
    Springer
    Queueing systems 2 (1987), S. 93-114 
    Details
    ISSN: 1572-9443
    Keywords: Roots ; batch service ; single server ; probability distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In their book, Chaudhry and Templeton [6] present a unified approach to many problems on bulk queues. Using their analytical approach, we show how to numerically evaluate steady-state probabilities and moments for number in system (or queue) at each of three time epochs — postdeparture, prearrival and random — for several bulk and nonbulk queues. The approach can be used for other problems in queueing theory, and for similar problems in the theories of dams, inventories, etc. The present study extends the computational results available in tables, such as those produced by Hillier and Yu [12], and has several potential applications. The method proposed is computationally efficient, accurate, and stable. It accommodates high values of the queueing parameters. Sample numerical results and graphs are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158395
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  • 4
    Electronic Resource
    Electronic Resource
    Computational analysis of single-server bulk-arrival queues: GIX/M/1 (1987)
    Springer
    Queueing systems 2 (1987), S. 173-185 
    Details
    ISSN: 1572-9443
    Keywords: Roots ; random group arrival ; single server ; probability distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper deals with numerical computations for the bulk-arrival queueing modelGI X/M/1. First an algorithm is developed to find the roots inside the unit circle of the characteristic equation for this model. These roots are then used to calculate both the moments and the steady-state distribution of the number of customers in the system at a pre-arrival epoch. These results are used to compute the distribution of the same random variable at post-departure and random epochs. Unifying the method used by Easton [7], we have extended its application to the special cases where the interarrival time distribution is deterministic or uniform, and to cases whereX has a given arbitrary distribution. We also improved on the various root-finding methods used by several previous authors so that high values of the parameters, in particular large batch sizes, can be investigated as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158398
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  • 5
    Electronic Resource
    Electronic Resource
    Micronutrient availability to cereals from calcareous soils (1979)
    Springer
    Plant and soil 52 (1979), S. 537-545 
    Details
    ISSN: 1573-5036
    Keywords: Copper ; Disc-plough ; Laminated layer ; Manganese ; Nitrogen ; Nutrient absorption ; Plough-pan ; Rotavator ; Subsoiler ; Weed ; Zinc
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The mechanism of higher grain production of wheat (Triticum aestivum L.) by four tillage methods was explored on a sandy calcareous soil of Sahl-Al Jafara, Libya, during the year 1976–77. Tillage methods increased grain yield and dry matter weight at the boot stage in the order of no-tillage〈rotovator=disc plough 〈 subsoiler. Rotovation to 15 cm and disc ploughing to 25 cm depth enhanced grain production mainly by eliminating weed competition. In both the cases, roots penetrated 〈 25 cm where plough-pan existed. Further yield increases by 50 cm deep subsoiling seems to be mainly explained by N and Cu rise in plants from their marginal to optimum levels and by reduction of Mn deficiency in plant shoots. Penetration of roots beyond the 25 cm plough-pan apparently resulted in higher absorption of these nutrients from leached or native soil supplies. Subsoiling also resulted in greater Zn concentration in plant shoots which, under marginal to deficient conditions, will also increase grain production.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02277949
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  • 6
    Electronic Resource
    Electronic Resource
    Computing steady-state queueing-time distributions of single-server queues:GI X /M/1 (1993)
    Springer
    Mathematical methods of operations research 37 (1993), S. 13-29 
    Details
    ISSN: 1432-5217
    Keywords: Queueing-Time Distribution ; Roots ; Computations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper presents a computationally efficient method to find the steady-state distributions of actual queueing times of the first customer, as well as of a randomly selected customer, of an arrival group for the queueing systemGI X /M/1, and hence the queueing-time distribution of a customer for the systemGI/E X /1. The distribution of virtual queueing time is also obtained. Approximate analysis based on one or more roots is also discussed. Though the exact detailed as well as approximate computations for a variety of interarrival-time distributions such as generalized Erlang, mixed generalized Erlang, hyperexponential, generalized hyperexponential, and deterministic have been carried out, only representative results in the form of tables have been appended. The results obtained should prove useful to queueing theorists, practitioners, and others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415525
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