- Fundamental questions in multiserver systems.
- An example of Markov chain modeling: an M/M/1/FCFS queue.
- A 1D Markov chain.
- A multidimensional Markov chain that appears in a multiserver analysis.
- Organization of Part I: Analytical tools for multiserver systems.
- The key idea in DR: dimensionality reduction (2D 1D).
- Organization of Part II: Performance analysis of multiserver systems.
- The
`SBCS-ID`policy. - The
`SBCS-CQ`policy. - A threshold-based policy for reducing switching costs in cycle stealing.
- The Beneficiary-Donor model.
- A PH distribution as the distribution of the time until absorption in a continuous time Markov chain.
- The Markov chain whose absorption time defines an -phase EC distribution.
- The Markov chain whose absorption time defines an extended EC distribution.
- Set as a function of the normalized moments.
- Characterizing via .
- Examples of PH distributions.
- A three-phase PH distribution.
- Subclasses of the PH distribution.
- Set and set .
- A classification of distributions.
- An implementation of the
`Simple`closed form solution. - Ideas in the
`Simple`solution. - An implementation of the
`Complete`closed form solution. - Ideas in the
`Complete`solution. - An implementation of the
`Positive`closed form solution. - Ideas in the
`Positive`solution. - Examples of multidimensional Markov chains that model multiserver systems.
- Markov chains for an M/M/2 queue with two preemptive priority classes.
- Dimensionality reduction of 2D Markov chain.
- Markov chains for an M/PH/2 queue with two preemptive priority classes.
- Markov chain on a finite state space for the high priority jobs in an M/PH/2 queue with two preemptive priority classes.
- 1D Markov chain for an M/PH/2 queue with two preemptive priority classes.
- FB, RFB, and GFB processes.
- Examples of QBD processes.
- Examples of Markovian arrival processes.
- QBD processes for MAP/M/1 queues.
- A MAP(2)
- Algorithms for calculating , 's, and other relevant matrices.
- FB process consisting of a foreground birth-and-death process and a background birth-and-death process.
- An example of an RFB process: Size-based task assignment with cycle stealing under immediate dispatching.
- Ideas in the RFB process.
- An example of an RFB process: Preemptive priority queue.
- The structure of the GFB process.
- An example of an GFB process: Threshold-based policy for reducing switching costs in cycle stealing.
- An example of a GFB process: Size-based task assignment with cycle stealing under central queue.
- An example of a GFB process: Nonpreemptive priority queue.
- Threshold-based policies for the Beneficiary-Donor model.
- Examples of GFB processes: Threshold-based policies for the Beneficiary-Donor model.
- An analysis of the FB process in Figure 3.13 via DR.
- An analysis of the GFB process via DR.
- A GFB process: Threshold-based policy for reducing switching costs in cycle stealing.
- An analysis of the GFB process in Figure 3.25 via DR.
- Background processes on a finite state space, obtained via DR-PI and DR-CI.
- Markov chains whose stationary probabilities are computed via DR in the analysis of an M/M/2 queue with two preemptive priority classes.
- Markov chains used to compute the response time in an M/M/2 queue with two preemptive priority classes.
- Accuracy of DR in the analysis of preemptive priority queues.
- Accuracy of DR, DR-PI, and DR-CI in predicting the first two moments of the queue length distributions.
- Accuracy of DR, DR-PI, and DR-CI at different loads.
- Accuracy of DR, DR-PI, and DR-CI at different job size configurations.
- Error in DR, DR-PI, and DR-CI when the busy period is approximated by an exponential distribution matching only the first moment.
- Running time of DR, when applied to an analysis of the preemptive priority queue.
- Running time of DR, DR-PI, and DR-CI, when applied to an analysis of
`SBCS-ID`. - How many servers are best in a single server (FCFS) system?
- How many servers are best when the two priority classes have the same mean job size?
- How many servers are best when the high priority jobs have a smaller mean job size?
- How many servers are best when the high priority class has a larger mean job size?
- Mean response time as a function of the number of servers.
- Comparison of DR with BB with respect to the question of ``how many servers are best?''
- Comparison of DR-A, MK-N, and BB approximations for M/PH/2 with 4 priority classes.
- Size-based task assignment with cycle stealing.
- Stability region for
`Dedicated`,`SBCS-ID`, and`SBCS-CQ`. - Mean response time of short jobs and long jobs under
`Dedicated`,`SBCS-ID`, and`SBCS-ID`. - Percentage change in the overall mean response time of
`SBCS-ID`and`SBCS-CQ`against`Dedicated`. - Effect of variability in long job size on the mean response time.
- A threshold-based policy for reducing switching costs in cycle stealing.
- A renewal cycle of the donor queue under the threshold-based policy for reducing switching costs in cycle stealing.
- Stability region for the threshold-based policy for reducing switching costs in cycle stealing.
- The mean response time for beneficiary jobs and donor jobs as a function of under cycle stealing and dedicated servers.
- The gain of beneficiary jobs and pain of donor jobs, and the effect of cycle stealing on the overall mean response time relative to dedicated servers: exponential distributions
- The gain of beneficiary jobs and pain of donor jobs, and the effect of cycle stealing on the overall mean response time relative to dedicated servers: PH distribution.
- The impact of the variability of donor job sizes on the mean response time of the beneficiary jobs.
- The mean response time for beneficiary jobs and donor jobs as a function of .
- Optimal values of and with respect to overall mean response time.
- The Beneficiary-Donor model.
- The T1 policy and the T2 policy.
- Stability conditions for the T1 policies and for the T2 policy.
- The mean response time under the T1 policy as a function of and the mean response time under the T2 policy as a function of , when .
- The mean response time under the T1 policy as a function of , and the mean response time under the T2 policy as a function of , when .
- Static robustness of single-threshold allocation policies.
- The T1T2 policy.
- Static robustness of the T1T2 policy.
- The ADT policy.
- Static robustness of the ADT policy.
- Comparison of the ADT policy with the T1 policy with respect to the mean response time.
- Dynamic robustness of the ADT policy and the T1 policy.
- Contact center architecture.
- A flow of routing policy design and capacity management/planning at a contact center.
- Virtual waiting time analysis.
- The Markov chain whose absorption time defines an Erlang-Exp distribution.
- The Markov chain whose absorption time defines an Exp-Erlang distribution.

Takayuki Osogami 2005-07-19