Approximate Behavior of Tandem Queues

1. Front Matter

   Pages N2-XI

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2. General Theory

   • Gordon F. Newell

   Pages 1-42

3. A Single Server

   • Gordon F. Newell

   Pages 43-89

4. Equilibrium Queue Distributions, Two Servers, μ0 = μ1 = μ2, Theory

   • Gordon F. Newell

   Pages 90-148

5. Equilibrium Queue Distributions, Two Servers μ0 = μ1 = μ2, Numerical Results

   • Gordon F. Newell

   Pages 149-217

6. Time-dependent Solutions, ∆0 = ∆1 = ∆2

   • Gordon F. Newell

   Pages 218-230

7. Laplace Transform Methods; Equilibrium Queue Distributions for n = 2, μ0 < μ1 ≠ μ2

   • Gordon F. Newell

   Pages 231-312

8. Equilibrium Queue Distributions; n = 2; μ1 < μ0 , μ2 ; c1 , c2 → ∞

   • Gordon F. Newell

   Pages 313-380

9. Epilogue

   • Gordon F. Newell

   Pages 381-402

10. Back Matter

    Pages 403-413

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The following monograph deals with the approximate stochastic behavior of a system consisting of a sequence of servers in series with finite storage between consecutive servers. The methods employ deterministic queueing and diffusion approximations which are valid under conditions in which the storages and the queue lengths are typically large compared with 1. One can disregard the fact that the customer counts must be integer valued and treat the queue as if it were a (stochastic) continuous fluid. In these approximations, it is not necessary to describe the detailed probability distribution of service times; it suffices simply to specify the rate of service and the variance rate (the variance of the number served per unit time). Specifically, customers are considered to originate from an infinite reservoir. They first pass through a server with service rate ~O' vari­ ance rate ~O' into a storage of finite capacity c . They then pass l through a server with service rate ~l' variance rate ~l' into a storage of capacity c ' etc., until finally, after passing through an nth server, 2 they go into an infinite reservoir (disappear). If any jth storage become , n , the service at the j-lth server is interrupted full j = 1, 2, and, of course, if a jth storage becomes empty the jth server is inter­ rupted; otherwise, services work at their maximum rate.

• Distribution
• Image
• Queues
• Warteschlange
• equilibrium
• evaluation
• merger
• probability
• probability distribution
• science and technology
• service
• value-at-risk

• Institute of Transportation Studies, University of California, Berkeley, USA

  Gordon F. Newell

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