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where T1, T2 are the service times for sources 1 and 2. |
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Queue behavior of the various common queue model types is summarized in Table ??. |
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6.5 Open-, Closed-, and Mixed-Queue Models |
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Open-queue models are the simplest queueing form. These models (at least as used here) assume: |
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1. Arrival rate independent of service rate. |
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2. As a consequence of (1), a queue of unbounded length as well as a (potentially) unbounded waiting time. |
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Many will recognize the suitability of open-queue models to contain highway congestion or bridge access situations, but will also recognize the unsuitability to computer systems. In a processor-memory interaction, the processor's request rate decreases as memory congestion increases. The arrival rate is a function of the total service time (including waiting time). This latter type of situation can be modeled by a queue with feedback. The system is initially offered a request rate (lo), but certain requests cannot immediately enter the server and are held in a queue. The requestor slows down to accommodate this and the arrival rate is now la (the achieved arrival ratesee Figure ??). |
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Figure 6.18
Capacity queues. |
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We call such systems closed queue (or a capacity queue) and designate them Qc. These queues usually have a bounded size and waiting time. |
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It is also possible for systems to behave as open-queueing systems up to a certain queue size, then they behave as closed queues. We call such systems mixed-queue systems. The assumptions made in developing the open-queue model might make it seem an unlikely candidate for memory systems modeling, yet its simplicity is attractive and it remains a useful first approximation to memory systems behavior. |
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