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... accurately, long waiting times arise due to the fact that the service times, i.e., the time a doctor talks to or examines patients, well described with a D IGI queue When visiting sulting a doctor ... stochastic The customer population requesting service These regime Are we dealing with an infinite or with a finite customer populat

Ngày tải lên: 15/12/2013, 08:15

... arrivals waiting in service Figure 2.2: The inside view of a job servicing system explain below At the queue on average X jobs arrive per time unit The time spent in the queue is the waiting time, ... (at 50% utilisation, the mean waiting time equals the mean service time) Consequently, for higher utilisations, the mean response time includes more than 50% of waiting Also observe that the cur...

Ngày tải lên: 15/12/2013, 08:15

... system consisting system of three computing nodes and a single voting node The three computing nodes generate results after which the voter decides upon the correct value (by selecting the answer ... is continuous Apart from those based on the above distinctions, we can also classify stochastic processes in another way We will so below, thereby taking the notation for the case of continuousti...

Ngày tải lên: 15/12/2013, 08:15

... cr2E[R2] First of all, we know that E[Ri] = s, Writing E[R] = criE[Ri] we obtain an expression E[Si] = E[S]/Ki, a + (1 - c~i)E[&] and substituting for E[R] as a function of ~1: E[R(w)] = al - ... 4.10, thereby again noting that if we change K, po will change as well (we therefore write po as a function In summary, we have of K below) - E[Z] (4.56) Instead of computing PO(K) explicitly, ... jo...

Ngày tải lên: 15/12/2013, 08:15

... 0.8 < the queueing moment as a Poisson density s < Calculating since p = XE[S] the second = and E[Sg] although E[S] = Am sfs(s)ds lating var[Si] values variance = 0, whenever Clearly, = so that ... job must be equal, we have E[ni+i] = E[ni] = E[n] Noting that we deal with independent from i, i.e., E[a] = E[ai] By a similar E[l(n)] Substituting this in (5.19) yields Poisson arrivals, argument,...

Ngày tải lên: 24/12/2013, 15:15

... waiting times (in seconds) in a computer center with non-preemptive and preemptive priorities waiting times for the two job classes For easeof comparison, we have also included the expected waiting ... we can compute the expected waiting times for increasing load, as indicated in Table 6.1 What can be observed is that even for small utilisations the average waiting time E[W] is significantly...

Ngày tải lên: 24/12/2013, 15:15

... p Knowing the probabilities ri, we can compute the expected waiting time for a customer as co E[W] = C riiE[S], (7.3) i=O by noting that for a customer arriving at a station with i customers ... over the role of p in the expression for the mean waiting time, we see that for small utilisations (when CJis much smaller than p) the waiting time is much lower than in the corresponding MIMI1 ... di...

Ngày tải lên: 24/12/2013, 15:15

... the repetitive CTMC structure; Substituting this solution in the repeating part of the global balance equations to derive the multiplicative constant p; Computing the solution of the “boundary probabilities” ... from a quadratic equation obtained by substituting the assumed geometric form in the repeating portion of the global balance equation: which, after rewriting the vectors pi in terms o...

Ngày tải lên: 24/12/2013, 15:15

... performance measure of interest is then the customer waiting time for queue i, i.e., Wi Most analytic models only provide insight into the average waiting time E[ Wi] When the queues are bounded, the ... order We distinguish three different ordering via a polling table l polling probability visit orders: a cyclic ordering, a Markovian ordering and an Cyclic polling In a cyclic visiting scheme...

Ngày tải lên: 24/12/2013, 15:15

... correctness of this result can be verified by substituting it in the global balance equations of the underlying CTMC From p all kinds of interesting performance measures can be obtained Notice that ... appropriate routing probabilities ri,j There are basically three operations that affect the traffic through the QN and which are illustrated in Figure 10.5: (a) the probabilistic splitting of a...

Ngày tải lên: 24/12/2013, 15:15

... digits; typically, using ordinary floating point numbers, such as those of the 64-bit IEEE 754 floating point number standard, does not suffice cl when evaluating large GNQNs! 11.4 Mean-value analysis-based ... fiD;% (11.18) i=l We now split this sum into two parts, one part accounting for all the states with ?zM = and one part accounting for all the states with nM > 0: M M-l ngZ(M-1,K) i=l T...

Ngày tải lên: 24/12/2013, 15:15

... load-dependent servers using the convolution scheme Consider a GNQN consisting of A4 MIMI1 stations with K customers As before, the routing probabilities are denoted ri,j and the state space Z(A4, K) ... paging cope in our models with routing of pages, whether In summary, or convolution the visit to reflect the of a model part, we have to assume that the routing even if less customers For j =...

Ngày tải lên: 24/12/2013, 15:15

... network with probability T+;~ Depending on which routing possi- bilities are present, the pairs (node, class) can be partitioned into so-called routing chains In many practical cases, class changes ... see below) A fraction ro;i,c of these arrivals arrive at queue i For every routing chain c E C (C is the set of all routing chains, NC = ICI), the following traffic equation where X& is determi...

Ngày tải lên: 24/12/2013, 15:15

... union of a set of input arcs (pointing from places to transitions), a set of output arcs (pointing from transitions to places) and a set of inhibitor arcs (pointing from places to transitions; ... more of them waiting (in comparison to those waiting of the other class) We can so by making the weights of AcqA and AcqB proportional to the number of customers of that class waiting If the printer...

Ngày tải lên: 24/12/2013, 15:15

... methods is that they aim at rewriting the system of equations in such a form that explicit expressions for the steady-state probabilities are obtained Typically, this rewriting (given N) elimination ... 0, for all j > i By repeating this procedure for increasing i, the linear system of equations is transformed, in N - steps, to an upper-triangular Uj,i Uj,i 15.1 Computing steady-state probabi...

Ngày tải lên: 21/01/2014, 20:20